Long Report

Final Project Long Report

This is the comprehensive long report for the final project of Stat 301-2. It contains all essential contents of the final project separated into four sections: the introduction of data and research questions, the exploratory data analysis, data modeling, and conclusion.

# Load Packages
library(tidyverse)
library(janitor)
library(skimr)
library(tidymodels)
library(corrplot)
library(lubridate)
library(lares)
library(corrr)
library(kableExtra)
library(naniar)
library(embed)

# set seed
set.seed(42)

Introduction

Dataset Overview

The project uses the dataset “COVID-19 Reported Patient Impact and Hospital Capacity by State Timeseries”. This dataset documents the COVID-19 related patient impact and hospital utilization as state-specific timeseries from 2020-01-01 to 2021-02-27. The dataset is obtained from Data.gov. The URL to the original data source is linked with the dataset name.

Note: The dataset is aggregated on a daily basis, and the version with dates ending at 2021-02-27 was the most recent version when the dataset was downloaded for this project. Thus, the link provided might be outdated with the most current version of the dataset.

The original dataset has 19520 rows, representing 19520 unique date and state combinations. There are 60 columns in the original dataset, representing 60 variables. The first column, state is a character type variable, and it represents the two digit state code. The second column is the date in ymd form. The remaining 58 variables are all numeric variables, such as critical_staffing_shortage_today_not_reported and inpatient_beds_coverage. They convey information regarding the capacity and utilization of the medical system and the patient impacts.

Research Questions

The ongoing COVID-19 pandemic has caused excess deaths and significant decline in life expectancy for the worldwide population. The pandemic has posed unprecedented challenges to the worldwide health systems. In particular, the United States is among the countries that are most affected by the pandemic. The stress on the health system leads to poor outcomes, such as high mortality and morbidity rates.[1] Thus, understanding the trends in hospital utilization and being able to predict future shortages are important for better resource management to reduce the inpatient mortality and morbidity that are caused either directly or indirectly by COVID-19.

Following the incentives above, my research question is to create a regression model to predict the number of hospitals having (reporting to have) a critical staffing shortage in a specific state at a given date based on the information regarding the current condition of COVID-19 related patient impact and hospital utilization in that state. The response variable is critical_staffing_shortage_today_yes - the number of hospitals reporting that they have a critical staffing shortage on the given day in a specific state.

Exploratory Data Analysis

Load Data

I first loaded in the unprocessed dataset, cleaned the names, and obtained an overview with the dataset API online and the interactive viewer:

# load in dataset
covid_data <- 
  read_csv("data/unprocessed/reported_hospital_utilization_timeseries_20210227_1306.csv") %>%
  clean_names()

Initial Tidying

Through initial inspection using the skim() function and the interactive viewer, I learned that the initial dataset has 60 variables. The data dictionary provided with the data source indicates that there are variables with repeated information. For instance, variables with name ending with _numerator and _demoninator are used to compute variables starting with percent_ or ending with _utilization. A specific example can be inpatient_beds_utilization_numerator, inpatient_beds_utilization_denominator, and inpatient_beds_utilization.

Also, some variables are by meaning not suitable to be used as predictors for my research question. First, by definition, variables critical_staffing_shortage_today_no (number of hospitals reporting as not having a critical staffing shortage today in this state) and critical_staffing_shortage_today_not_reported (number of hospitals not reporting staffing shortage today status in this state) should be known at the same time with the outcome variable critical_staffing_shortage_today_yes. If we know critical_staffing_shortage_today_yes, we can also know the values of critical_staffing_shortage_today_no and critical_staffing_shortage_today_not_reported through linear combination based on the total number of reports received and the number of hospitals in the state from open online resources. Thus, it does not make sense to use critical_staffing_shortage_today_no and critical_staffing_shortage_today_not_reported as predictors. Also, since the aim of this research project is to predict the situation of critical staff shortage in the future, variables starting with critical_staffing_shortage_anticipated_within_week (number of hospitals anticipating / not anticipating to have staff shortage within a week) are more suitable to be used as potential response variables rather than predictors. Also, these variables are time lagged with the other variables, and the time range “within a week” is quite ambiguous in the given definitions from the dataset API (can be from 1 to 7 days). Thus, I chose to not include variables starting with critical_staffing_shortage_anticipated_within_week as predictors. Before further data analysis, I filtered out variables that are not going to be used as predictors from the dataset.

# filter out "disqualified" predictors
covid_data <- 
  covid_data %>% 
  select(-ends_with(c("_numerator", "_denominator",
                      "_no", "_not_reported", "within_week_yes")))

After filtering, 45 variables are left in the dataset including the potential outcome variable critical_staffing_shortage_today_yes.

Correlation

Before examining the missing data, I explored the correlations between variables for selecting predictors. I created a correlation matrix using methods from the corrplot package. Since state will definitely be used as a predictor, and it is not numeric, I did not include it in the analysis of correlations. Also, since the dataset is a time series, date is a variable of special focus. Its correlation with the response variable is explored individually in the “Exploring Timeseries” section. To avoid problems caused by missing data, I filtered out rows with NA values when creating the correlation matrix The code for creating the correlation matrix is presented below:

# create correlation matrix
corr_matrix_tot <- covid_data %>% 
  # unselect non-numeric type variables
  select(-c(state, date)) %>% 
  # remove rows with missing data
  drop_na() %>%
  cor()

Predictor Selection

To determine whether all 44 variables should be used as predictors, I explored the correlation between each variable and the response variable critical_staffing_shortage_today_yes by extracting the corresponding row (the first row), pivoting it to be longer, and arranging the correlation coefficients in descending order. For presentation of the results, I formatted it into a scrollable box using methods from the kableExtra package. To check whether there are variables with near perfect collinearity with the response variable that will cause problem in the later modeling process, I also showed the number of rows with greater than 0.9 correlation coefficients.

# correlations with response variable
# arrange in ascending order of correlation coefficient
corr_response <- corr_matrix_tot %>% 
  as_tibble() %>% 
  # select the column showing the correlation with the outcome var
  head(1) %>% 
  # pivoting, make a character column of variables' names
  # and a numeric column of values of the correlation coefficients
  pivot_longer(everything(), 
               names_to = "variable", values_to = "correlation") %>%
  arrange(desc(correlation))

# show the correlation with the response variable in a scrollable box
kbl(corr_response) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "200px")

variable	correlation
critical_staffing_shortage_today_yes	1.0000000
hospital_onset_covid_coverage	0.8268080
previous_day_admission_pediatric_covid_suspected_coverage	0.8239467
previous_day_admission_pediatric_covid_confirmed_coverage	0.8214313
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.8194406
inpatient_beds_utilization_coverage	0.8193939
inpatient_beds_coverage	0.8191663
inpatient_beds_used_coverage	0.8185606
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8181620
staffed_icu_adult_patients_confirmed_covid_coverage	0.8181605
total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.8180883
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8173769
total_adult_patients_hospitalized_confirmed_covid_coverage	0.8172957
previous_day_admission_adult_covid_suspected_coverage	0.8167954
inpatient_bed_covid_utilization_coverage	0.8160930
previous_day_admission_adult_covid_confirmed_coverage	0.8160037
percent_of_inpatients_with_covid_coverage	0.8155671
staffed_adult_icu_bed_occupancy_coverage	0.8154488
total_staffed_adult_icu_beds_coverage	0.8147879
adult_icu_bed_covid_utilization_coverage	0.8147257
adult_icu_bed_utilization_coverage	0.8144147
inpatient_beds_used_covid_coverage	0.8116209
staffed_icu_adult_patients_confirmed_covid	0.8111936
staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8056927
total_adult_patients_hospitalized_confirmed_covid	0.7404814
total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7391462
inpatient_beds_used_covid	0.7340499
previous_day_admission_adult_covid_confirmed	0.7261764
staffed_adult_icu_bed_occupancy	0.6997067
total_staffed_adult_icu_beds	0.6671198
inpatient_beds_used	0.6454002
inpatient_beds	0.6281196
total_pediatric_patients_hospitalized_confirmed_covid	0.6220859
previous_day_admission_adult_covid_suspected	0.6089723
previous_day_admission_pediatric_covid_confirmed	0.5533083
adult_icu_bed_covid_utilization	0.4201469
inpatient_bed_covid_utilization	0.4104020
percent_of_inpatients_with_covid	0.3900766
previous_day_admission_pediatric_covid_suspected	0.3833342
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.3417573
inpatient_beds_utilization	0.1823904
hospital_onset_covid	0.1032068
adult_icu_bed_utilization	0.0770885

# number of variables with relatively weak correlations with the outcome
corr_response %>% 
  filter(correlation >= 0.9) %>% 
  nrow()

## [1] 1

As shown above by the tibble, only one variable has perfect correlation coefficient - the response variable itself. Thus, there is no predictor variables with near perfect correlation with the response variable. The variables most correlated with the outcome variable have correlation coefficient around 0.82.

Correlation between Predictors

After examining the correlation with the response variable, I continued to investigate the correlations between the predictors.

To focus on the correlations between predictors, I excluded the outcome variable critical_staffing_shortage_today_yes and temporarily turned the non-numeric type variables state and date into numeric type variables. Afterwards, I used methods from the corrr package to show the correlations between the predictors. To do so, I first created a correlation matrix with the correlate() method from the corrr package. Then, I turn it into a tibble. Later, I arranged the valid answers in descending order of the correlation variable value - representing the correlation coefficient. Also, for the convenience of presentation and exploration, I filtered out rows with NA correlation values. Since the even rows (row 2, row 4, etc.) just repeat the information in the previous odd rows with the order of the two variables reversed, I removed the even rows from the resulting tibble. Same as above, I presented the results as a scrollable box.

# correlations between predictors
corr_pred <- covid_data %>% 
  # unselect outcome variable
  select(-c(critical_staffing_shortage_today_yes)) %>% 
  # temporarily change `state` and `date` to type numeric
  mutate(date = as.numeric(date),
         # first turn state into a factor
         # then turn it into a numeric variable
         # with values determined by factor levels
         state = as.numeric(as.factor(state))) %>%
  # remove rows with missing data
  drop_na() %>%
  # correlation matrix
  correlate() %>% 
  # turn into a tibble
  stretch() %>% 
  rename("correlation" = "r") %>% 
  # remove rows with invalid result
  # the `NA` values are the correlation of one var with itself
  # in this case
  filter(!is.na(correlation)) %>% 
  # arranging in descending order
  arrange(desc(correlation))

# remove even rows
# they just repeat the info of the odd rows above them
corr_pred <- corr_pred %>% 
  # temporary var `row_id` to help the removing process
  mutate(row_id = row_number()) %>% 
  # filter out even rows
  filter(!row_id %% 2 == 0) %>% 
  # remove temporary var
  select(-row_id)

# show the correlations between predictors in a scrollable box
kbl(corr_pred) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "200px")

x	y	correlation
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9996887
inpatient_beds_used_coverage	inpatient_beds_utilization_coverage	0.9995873
total_staffed_adult_icu_beds_coverage	adult_icu_bed_utilization_coverage	0.9995520
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_utilization_coverage	0.9992595
staffed_adult_icu_bed_occupancy_coverage	total_staffed_adult_icu_beds_coverage	0.9991530
adult_icu_bed_covid_utilization_coverage	adult_icu_bed_utilization_coverage	0.9991155
inpatient_beds_coverage	inpatient_beds_utilization_coverage	0.9991039
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9991014
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9990155
total_staffed_adult_icu_beds_coverage	adult_icu_bed_covid_utilization_coverage	0.9989580
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9989385
percent_of_inpatients_with_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9988549
inpatient_beds_coverage	inpatient_beds_used_coverage	0.9986980
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_covid_utilization_coverage	0.9982268
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9971256
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9970327
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9965775
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9962535
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9960787
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9959898
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9959042
staffed_icu_adult_patients_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_covid	0.9958744
previous_day_admission_pediatric_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9957961
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9957329
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9955322
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9953369
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9953174
inpatient_beds_used_coverage	percent_of_inpatients_with_covid_coverage	0.9952513
inpatient_beds_utilization_coverage	percent_of_inpatients_with_covid_coverage	0.9948947
inpatient_beds_coverage	inpatient_bed_covid_utilization_coverage	0.9948889
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9948749
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9948272
inpatient_beds_utilization_coverage	inpatient_bed_covid_utilization_coverage	0.9944642
hospital_onset_covid_coverage	inpatient_beds_coverage	0.9943271
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9941344
inpatient_beds_used_coverage	inpatient_bed_covid_utilization_coverage	0.9941095
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9940599
total_pediatric_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9940044
hospital_onset_covid_coverage	inpatient_beds_utilization_coverage	0.9939023
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9938344
inpatient_beds_used_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9938268
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9937893
inpatient_beds_coverage	percent_of_inpatients_with_covid_coverage	0.9937467
inpatient_beds_used_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9937332
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9936703
total_adult_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9936323
hospital_onset_covid_coverage	inpatient_beds_used_coverage	0.9935837
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9934683
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9933185
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9932943
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9932664
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9932300
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9931901
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9931802
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9931158
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9928667
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9927745
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9927368
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9926262
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9923912
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9921286
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9919042
inpatient_beds_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9918265
inpatient_beds_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9918234
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9917794
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9917270
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9917232
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9917030
previous_day_admission_adult_covid_confirmed_coverage	inpatient_beds_utilization_coverage	0.9916734
previous_day_admission_adult_covid_suspected_coverage	inpatient_beds_utilization_coverage	0.9916545
inpatient_beds_used_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9915721
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9915355
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9915328
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9915288
inpatient_beds_used_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9914595
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9912689
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9911244
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9909643
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9909582
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9909015
hospital_onset_covid_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9908878
hospital_onset_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9908083
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9907483
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9907325
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9906539
hospital_onset_covid_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9905503
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9905158
inpatient_beds	inpatient_beds_used	0.9904805
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9904770
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9904270
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9902753
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9902579
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9902323
inpatient_beds_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9901904
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9901272
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9900715
staffed_icu_adult_patients_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9900656
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9900138
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9899790
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_covid	0.9899383
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9898924
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9898156
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9897731
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9897448
hospital_onset_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9897429
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9897391
staffed_adult_icu_bed_occupancy_coverage	inpatient_beds_utilization_coverage	0.9897328
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9897189
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9897160
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9896769
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9896244
previous_day_admission_pediatric_covid_suspected_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9895801
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9895620
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9894987
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9894330
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9893665
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9893092
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_covid_utilization_coverage	0.9893031
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9891756
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_covid_utilization_coverage	0.9891555
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_utilization_coverage	0.9891549
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_utilization_coverage	0.9891015
previous_day_admission_pediatric_covid_confirmed_coverage	total_staffed_adult_icu_beds_coverage	0.9890652
previous_day_admission_pediatric_covid_suspected_coverage	total_staffed_adult_icu_beds_coverage	0.9890076
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9888732
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9888182
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9887556
inpatient_beds_used_coverage	inpatient_beds_used_covid_coverage	0.9887502
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9886461
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9884399
inpatient_beds_coverage	inpatient_beds_used_covid_coverage	0.9884179
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9884133
inpatient_beds_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9884107
inpatient_beds_coverage	total_staffed_adult_icu_beds_coverage	0.9883926
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9883211
previous_day_admission_adult_covid_suspected_coverage	inpatient_bed_covid_utilization_coverage	0.9882861
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_beds_utilization_coverage	0.9882223
inpatient_beds_used_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9881351
previous_day_admission_adult_covid_confirmed_coverage	inpatient_bed_covid_utilization_coverage	0.9881015
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9878637
inpatient_beds_used_covid_coverage	inpatient_beds_utilization_coverage	0.9878376
total_staffed_adult_icu_beds_coverage	inpatient_beds_utilization_coverage	0.9878079
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9877358
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9875735
staffed_icu_adult_patients_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9874270
previous_day_admission_adult_covid_suspected_coverage	percent_of_inpatients_with_covid_coverage	0.9874260
previous_day_admission_adult_covid_suspected_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9873919
previous_day_admission_adult_covid_confirmed_coverage	percent_of_inpatients_with_covid_coverage	0.9873715
previous_day_admission_adult_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9871433
inpatient_beds_coverage	adult_icu_bed_utilization_coverage	0.9869770
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9869622
staffed_adult_icu_bed_occupancy_coverage	inpatient_bed_covid_utilization_coverage	0.9866998
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9866746
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9865912
inpatient_beds_utilization_coverage	adult_icu_bed_utilization_coverage	0.9865560
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9864739
hospital_onset_covid_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9864464
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9859720
inpatient_beds_coverage	adult_icu_bed_covid_utilization_coverage	0.9858677
inpatient_beds_utilization_coverage	adult_icu_bed_covid_utilization_coverage	0.9856891
inpatient_beds_used_coverage	total_staffed_adult_icu_beds_coverage	0.9855934
inpatient_beds_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9855601
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_beds_utilization_coverage	0.9854267
previous_day_admission_adult_covid_suspected_coverage	total_staffed_adult_icu_beds_coverage	0.9853724
hospital_onset_covid_coverage	inpatient_beds_used_covid_coverage	0.9852947
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9851906
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_bed_covid_utilization_coverage	0.9851047
previous_day_admission_adult_covid_confirmed_coverage	total_staffed_adult_icu_beds_coverage	0.9850113
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_utilization_coverage	0.9847953
hospital_onset_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9847691
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9847645
staffed_adult_icu_bed_occupancy_coverage	percent_of_inpatients_with_covid_coverage	0.9847005
total_pediatric_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9845441
total_staffed_adult_icu_beds_coverage	inpatient_bed_covid_utilization_coverage	0.9845177
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_utilization_coverage	0.9844332
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_covid_utilization_coverage	0.9843965
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9843849
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9843551
inpatient_beds_used_coverage	adult_icu_bed_utilization_coverage	0.9841352
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9840972
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9840833
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9840409
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9840216
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9839811
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_covid_utilization_coverage	0.9837723
hospital_onset_covid_coverage	adult_icu_bed_utilization_coverage	0.9837721
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9837460
total_adult_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9837270
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9837183
hospital_onset_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9836920
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9835507
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9834334
inpatient_bed_covid_utilization_coverage	adult_icu_bed_utilization_coverage	0.9834001
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9831954
inpatient_beds_used_coverage	adult_icu_bed_covid_utilization_coverage	0.9831770
previous_day_admission_pediatric_covid_suspected_coverage	percent_of_inpatients_with_covid_coverage	0.9830427
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9830395
inpatient_bed_covid_utilization_coverage	adult_icu_bed_covid_utilization_coverage	0.9829885
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9826923
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_bed_covid_utilization_coverage	0.9824130
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9823367
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9823068
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9820894
total_staffed_adult_icu_beds_coverage	percent_of_inpatients_with_covid_coverage	0.9818945
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_covid	0.9812115
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9810497
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9810439
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9808029
percent_of_inpatients_with_covid_coverage	adult_icu_bed_utilization_coverage	0.9806204
previous_day_admission_pediatric_covid_confirmed_coverage	percent_of_inpatients_with_covid_coverage	0.9804751
percent_of_inpatients_with_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9800667
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9788504
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_covid	0.9767366
inpatient_beds	total_staffed_adult_icu_beds	0.9763855
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9761728
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9760262
percent_of_inpatients_with_covid	inpatient_bed_covid_utilization	0.9751065
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9747235
inpatient_beds_used	total_staffed_adult_icu_beds	0.9745122
inpatient_beds_used_covid_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9727648
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9726784
inpatient_beds_used_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9696686
inpatient_beds_used_covid_coverage	adult_icu_bed_utilization_coverage	0.9676645
inpatient_beds_used_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9671422
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid	0.9641409
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9624642
inpatient_beds_used_covid	previous_day_admission_adult_covid_confirmed	0.9551771
staffed_adult_icu_bed_occupancy	total_staffed_adult_icu_beds	0.9490643
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_covid	0.9448888
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9409511
inpatient_beds_used	staffed_adult_icu_bed_occupancy	0.9367275
inpatient_beds	staffed_adult_icu_bed_occupancy	0.9311894
inpatient_beds_coverage	total_staffed_adult_icu_beds	0.8929508
total_staffed_adult_icu_beds	inpatient_beds_utilization_coverage	0.8928735
staffed_adult_icu_bed_occupancy_coverage	total_staffed_adult_icu_beds	0.8926633
inpatient_beds_used_coverage	total_staffed_adult_icu_beds	0.8922869
total_staffed_adult_icu_beds	total_staffed_adult_icu_beds_coverage	0.8907671
total_adult_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds	0.8899950
total_staffed_adult_icu_beds	adult_icu_bed_utilization_coverage	0.8899458
staffed_icu_adult_patients_confirmed_covid_coverage	total_staffed_adult_icu_beds	0.8896342
previous_day_admission_adult_covid_confirmed_coverage	total_staffed_adult_icu_beds	0.8895434
total_staffed_adult_icu_beds	inpatient_bed_covid_utilization_coverage	0.8882326
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds	0.8879348
total_staffed_adult_icu_beds	percent_of_inpatients_with_covid_coverage	0.8878171
percent_of_inpatients_with_covid	adult_icu_bed_covid_utilization	0.8875535
total_pediatric_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds	0.8868836
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds	0.8867600
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds	0.8865948
previous_day_admission_adult_covid_suspected_coverage	total_staffed_adult_icu_beds	0.8863998
total_staffed_adult_icu_beds	adult_icu_bed_covid_utilization_coverage	0.8844929
staffed_adult_icu_bed_occupancy	staffed_adult_icu_bed_occupancy_coverage	0.8843635
staffed_adult_icu_bed_occupancy	total_staffed_adult_icu_beds_coverage	0.8826871
staffed_adult_icu_bed_occupancy	adult_icu_bed_utilization_coverage	0.8824888
inpatient_beds	inpatient_beds_coverage	0.8815979
staffed_adult_icu_bed_occupancy	inpatient_beds_utilization_coverage	0.8815529
inpatient_beds_coverage	staffed_adult_icu_bed_occupancy	0.8814363
inpatient_beds	inpatient_beds_utilization_coverage	0.8813697
inpatient_beds	inpatient_beds_used_coverage	0.8812389
inpatient_beds_used_coverage	staffed_adult_icu_bed_occupancy	0.8810369
inpatient_beds_used_covid_coverage	total_staffed_adult_icu_beds	0.8806571
staffed_adult_icu_bed_occupancy	staffed_icu_adult_patients_confirmed_covid_coverage	0.8803818
hospital_onset_covid_coverage	total_staffed_adult_icu_beds	0.8799563
staffed_adult_icu_bed_occupancy	total_adult_patients_hospitalized_confirmed_covid_coverage	0.8795188
inpatient_bed_covid_utilization	adult_icu_bed_covid_utilization	0.8793629
previous_day_admission_adult_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy	0.8786615
previous_day_admission_pediatric_covid_suspected_coverage	total_staffed_adult_icu_beds	0.8785858
staffed_adult_icu_bed_occupancy	adult_icu_bed_covid_utilization_coverage	0.8783562
staffed_adult_icu_bed_occupancy	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.8782024
staffed_adult_icu_bed_occupancy	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8781354
staffed_adult_icu_bed_occupancy	inpatient_bed_covid_utilization_coverage	0.8779114
staffed_adult_icu_bed_occupancy	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.8778637
inpatient_beds_used	inpatient_beds_used_coverage	0.8778151
staffed_adult_icu_bed_occupancy	percent_of_inpatients_with_covid_coverage	0.8775814
inpatient_beds	inpatient_bed_covid_utilization_coverage	0.8775758
inpatient_beds	total_adult_patients_hospitalized_confirmed_covid_coverage	0.8774280
previous_day_admission_pediatric_covid_confirmed_coverage	total_staffed_adult_icu_beds	0.8773660
inpatient_beds_used	inpatient_beds_utilization_coverage	0.8772970
inpatient_beds	percent_of_inpatients_with_covid_coverage	0.8772342
inpatient_beds	staffed_adult_icu_bed_occupancy_coverage	0.8769974
staffed_adult_icu_bed_occupancy	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8766199
inpatient_beds_coverage	inpatient_beds_used	0.8765867
previous_day_admission_adult_covid_suspected_coverage	staffed_adult_icu_bed_occupancy	0.8763243
inpatient_beds	previous_day_admission_adult_covid_confirmed_coverage	0.8761786
inpatient_beds	staffed_icu_adult_patients_confirmed_covid_coverage	0.8756574
inpatient_beds	total_staffed_adult_icu_beds_coverage	0.8746640
inpatient_beds	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8746058
inpatient_beds	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8742734
inpatient_beds_used	percent_of_inpatients_with_covid_coverage	0.8740286
inpatient_beds	adult_icu_bed_utilization_coverage	0.8739165
inpatient_beds_used	total_adult_patients_hospitalized_confirmed_covid_coverage	0.8737834
inpatient_beds_used	staffed_adult_icu_bed_occupancy_coverage	0.8737033
inpatient_beds	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.8735324
inpatient_beds	previous_day_admission_adult_covid_suspected_coverage	0.8734003
inpatient_beds_used	inpatient_bed_covid_utilization_coverage	0.8730438
previous_day_admission_pediatric_covid_suspected_coverage	staffed_adult_icu_bed_occupancy	0.8728615
inpatient_beds_used	previous_day_admission_adult_covid_confirmed_coverage	0.8727099
hospital_onset_covid_coverage	staffed_adult_icu_bed_occupancy	0.8723925
inpatient_beds	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.8720478
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy	0.8719987
inpatient_beds	inpatient_beds_used_covid_coverage	0.8717921
inpatient_beds_used	staffed_icu_adult_patients_confirmed_covid_coverage	0.8717725
inpatient_beds_used	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8710108
inpatient_beds_used	total_staffed_adult_icu_beds_coverage	0.8708234
inpatient_beds_used	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8703463
inpatient_beds_used	adult_icu_bed_utilization_coverage	0.8701790
hospital_onset_covid_coverage	inpatient_beds	0.8700887
inpatient_beds_used	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.8699534
inpatient_beds_used_covid_coverage	staffed_adult_icu_bed_occupancy	0.8696838
inpatient_beds_used	previous_day_admission_adult_covid_suspected_coverage	0.8696258
inpatient_beds	adult_icu_bed_covid_utilization_coverage	0.8689524
inpatient_beds_used	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.8681326
inpatient_beds_used	inpatient_beds_used_covid_coverage	0.8679603
hospital_onset_covid_coverage	inpatient_beds_used	0.8664262
inpatient_beds	previous_day_admission_pediatric_covid_suspected_coverage	0.8655226
inpatient_beds_used	adult_icu_bed_covid_utilization_coverage	0.8654814
inpatient_beds	previous_day_admission_pediatric_covid_confirmed_coverage	0.8653124
inpatient_beds_used	previous_day_admission_pediatric_covid_confirmed_coverage	0.8626993
inpatient_beds_used	previous_day_admission_pediatric_covid_suspected_coverage	0.8623484
staffed_adult_icu_bed_occupancy	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8503833
staffed_adult_icu_bed_occupancy	staffed_icu_adult_patients_confirmed_covid	0.8367829
staffed_adult_icu_bed_occupancy	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.8360174
previous_day_admission_adult_covid_suspected	total_staffed_adult_icu_beds	0.8346474
inpatient_beds_used_covid	staffed_adult_icu_bed_occupancy	0.8296966
inpatient_beds_used	previous_day_admission_adult_covid_suspected	0.8267127
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_staffed_adult_icu_beds	0.8260014
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_staffed_adult_icu_beds	0.8209452
inpatient_beds	previous_day_admission_adult_covid_suspected	0.8198400
staffed_icu_adult_patients_confirmed_and_suspected_covid	adult_icu_bed_utilization_coverage	0.8167879
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_staffed_adult_icu_beds_coverage	0.8164589
staffed_icu_adult_patients_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization_coverage	0.8156544
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8155066
inpatient_beds_used_covid	total_staffed_adult_icu_beds	0.8144661
inpatient_beds_used	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8137566
staffed_adult_icu_bed_occupancy	total_adult_patients_hospitalized_confirmed_covid	0.8129968
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8115039
inpatient_beds_used	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.8114377
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8114046
staffed_icu_adult_patients_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_covid_coverage	0.8113524
staffed_icu_adult_patients_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.8105522
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.8101963
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8100461
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8096451
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.8094759
staffed_icu_adult_patients_confirmed_and_suspected_covid	inpatient_beds_utilization_coverage	0.8094583
previous_day_admission_adult_covid_confirmed	staffed_adult_icu_bed_occupancy	0.8093352
inpatient_beds_used	inpatient_beds_used_covid	0.8085211
staffed_icu_adult_patients_confirmed_and_suspected_covid	inpatient_bed_covid_utilization_coverage	0.8078918
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8078478
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.8072454
staffed_icu_adult_patients_confirmed_covid	total_staffed_adult_icu_beds	0.8072143
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8071111
staffed_icu_adult_patients_confirmed_and_suspected_covid	percent_of_inpatients_with_covid_coverage	0.8054450
staffed_icu_adult_patients_confirmed_covid	adult_icu_bed_utilization_coverage	0.8053813
staffed_icu_adult_patients_confirmed_covid	total_staffed_adult_icu_beds_coverage	0.8046986
staffed_icu_adult_patients_confirmed_covid	adult_icu_bed_covid_utilization_coverage	0.8041183
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_covid	0.8033597
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8022420
previous_day_admission_adult_covid_suspected	staffed_adult_icu_bed_occupancy	0.8022292
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.8011069
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid	0.7999526
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid	0.7997813
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.7997717
staffed_icu_adult_patients_confirmed_covid	staffed_icu_adult_patients_confirmed_covid_coverage	0.7994885
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	staffed_icu_adult_patients_confirmed_covid	0.7981984
inpatient_beds	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.7973330
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7971903
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_covid	0.7970831
staffed_icu_adult_patients_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7959160
inpatient_beds_used	staffed_icu_adult_patients_confirmed_covid	0.7957057
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_covid	0.7955378
staffed_icu_adult_patients_confirmed_covid	inpatient_beds_utilization_coverage	0.7953364
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7944421
staffed_icu_adult_patients_confirmed_covid	inpatient_bed_covid_utilization_coverage	0.7933621
staffed_icu_adult_patients_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7933613
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_covid	0.7926255
inpatient_beds	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7907795
staffed_icu_adult_patients_confirmed_covid	percent_of_inpatients_with_covid_coverage	0.7906118
total_adult_patients_hospitalized_confirmed_covid	total_staffed_adult_icu_beds	0.7900725
previous_day_admission_adult_covid_confirmed	total_staffed_adult_icu_beds	0.7899417
inpatient_beds	inpatient_beds_used_covid	0.7890451
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid	0.7881750
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_covid	0.7870725
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid	0.7868403
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_suspected	0.7806745
inpatient_beds_used	total_adult_patients_hospitalized_confirmed_covid	0.7802740
inpatient_beds_used	previous_day_admission_adult_covid_confirmed	0.7786664
previous_day_admission_adult_covid_suspected	percent_of_inpatients_with_covid_coverage	0.7785060
inpatient_beds_used_coverage	previous_day_admission_adult_covid_suspected	0.7776318
inpatient_beds	staffed_icu_adult_patients_confirmed_covid	0.7765952
previous_day_admission_adult_covid_suspected	inpatient_bed_covid_utilization_coverage	0.7759238
previous_day_admission_adult_covid_suspected	inpatient_beds_utilization_coverage	0.7749742
inpatient_beds_coverage	previous_day_admission_adult_covid_suspected	0.7742597
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_adult_covid_suspected	0.7738541
previous_day_admission_adult_covid_suspected	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7726475
previous_day_admission_adult_covid_suspected	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7725614
previous_day_admission_adult_covid_suspected	previous_day_admission_adult_covid_suspected_coverage	0.7718101
previous_day_admission_adult_covid_suspected	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7714807
previous_day_admission_adult_covid_suspected	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7690242
total_adult_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_utilization_coverage	0.7663710
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_staffed_adult_icu_beds_coverage	0.7656418
previous_day_admission_adult_covid_suspected	staffed_adult_icu_bed_occupancy_coverage	0.7655101
hospital_onset_covid_coverage	previous_day_admission_adult_covid_suspected	0.7654120
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7646281
total_adult_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization_coverage	0.7641951
previous_day_admission_adult_covid_confirmed	adult_icu_bed_utilization_coverage	0.7633518
previous_day_admission_adult_covid_suspected	staffed_icu_adult_patients_confirmed_covid_coverage	0.7629962
previous_day_admission_adult_covid_suspected	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.7626616
previous_day_admission_adult_covid_confirmed	total_staffed_adult_icu_beds_coverage	0.7623118
previous_day_admission_adult_covid_confirmed	adult_icu_bed_covid_utilization_coverage	0.7619552
previous_day_admission_adult_covid_suspected	total_staffed_adult_icu_beds_coverage	0.7610622
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7604901
previous_day_admission_adult_covid_confirmed	staffed_adult_icu_bed_occupancy_coverage	0.7597186
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7597066
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7592143
previous_day_admission_adult_covid_suspected	adult_icu_bed_utilization_coverage	0.7588531
inpatient_beds	total_adult_patients_hospitalized_confirmed_covid	0.7588429
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7583427
previous_day_admission_adult_covid_confirmed	previous_day_admission_pediatric_covid_confirmed_coverage	0.7579987
previous_day_admission_adult_covid_confirmed	previous_day_admission_pediatric_covid_suspected_coverage	0.7577824
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7576091
previous_day_admission_adult_covid_suspected	adult_icu_bed_covid_utilization_coverage	0.7574684
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7572249
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7567770
previous_day_admission_adult_covid_suspected	previous_day_admission_pediatric_covid_confirmed_coverage	0.7566453
inpatient_beds_used_covid	adult_icu_bed_utilization_coverage	0.7563306
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7559670
inpatient_beds_used_covid	total_staffed_adult_icu_beds_coverage	0.7559097
inpatient_beds_used_covid	staffed_adult_icu_bed_occupancy_coverage	0.7556873
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7551581
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7551456
previous_day_admission_adult_covid_suspected	previous_day_admission_pediatric_covid_suspected_coverage	0.7551117
total_adult_patients_hospitalized_confirmed_and_suspected_covid	inpatient_bed_covid_utilization_coverage	0.7550999
total_adult_patients_hospitalized_confirmed_and_suspected_covid	inpatient_beds_utilization_coverage	0.7549837
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7549421
inpatient_beds	previous_day_admission_adult_covid_confirmed	0.7548846
inpatient_beds_used_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.7543942
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_covid_coverage	0.7542885
inpatient_beds_used_covid	adult_icu_bed_covid_utilization_coverage	0.7539424
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7529395
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_covid_coverage	0.7528555
inpatient_beds_used_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7527204
total_adult_patients_hospitalized_confirmed_and_suspected_covid	percent_of_inpatients_with_covid_coverage	0.7525802
inpatient_beds_used_covid	inpatient_beds_used_covid_coverage	0.7525543
inpatient_beds_used_covid	previous_day_admission_pediatric_covid_confirmed_coverage	0.7525213
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7524294
inpatient_beds_used_covid	inpatient_bed_covid_utilization_coverage	0.7517938
inpatient_beds_coverage	inpatient_beds_used_covid	0.7513156
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.7512909
previous_day_admission_adult_covid_suspected	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.7512279
inpatient_beds_used_covid	inpatient_beds_utilization_coverage	0.7511308
inpatient_beds_used_covid	previous_day_admission_pediatric_covid_suspected_coverage	0.7510784
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.7510394
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.7509444
hospital_onset_covid_coverage	inpatient_beds_used_covid	0.7508784
inpatient_beds_used_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7506398
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7501964
total_adult_patients_hospitalized_confirmed_covid	adult_icu_bed_utilization_coverage	0.7496576
inpatient_beds_used_covid	percent_of_inpatients_with_covid_coverage	0.7495791
inpatient_beds_used_coverage	inpatient_beds_used_covid	0.7491352
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7490853
hospital_onset_covid_coverage	previous_day_admission_adult_covid_confirmed	0.7489778
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7487361
total_adult_patients_hospitalized_confirmed_covid	total_staffed_adult_icu_beds_coverage	0.7485510
staffed_icu_adult_patients_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.7485184
total_adult_patients_hospitalized_confirmed_covid	adult_icu_bed_covid_utilization_coverage	0.7477717
previous_day_admission_adult_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7477560
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7465891
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7465162
previous_day_admission_adult_covid_confirmed	inpatient_beds_utilization_coverage	0.7458567
inpatient_beds_coverage	previous_day_admission_adult_covid_confirmed	0.7457229
previous_day_admission_adult_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7450670
previous_day_admission_adult_covid_confirmed	previous_day_admission_adult_covid_confirmed_coverage	0.7445190
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7442349
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7437141
inpatient_beds_used_covid	previous_day_admission_adult_covid_confirmed_coverage	0.7435709
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7434248
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7433776
previous_day_admission_adult_covid_confirmed	inpatient_bed_covid_utilization_coverage	0.7429348
inpatient_beds_used_coverage	previous_day_admission_adult_covid_confirmed	0.7423323
previous_day_admission_adult_covid_confirmed	previous_day_admission_adult_covid_suspected_coverage	0.7422994
total_adult_patients_hospitalized_confirmed_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.7421283
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7406762
inpatient_beds_used_covid	previous_day_admission_adult_covid_suspected_coverage	0.7405645
total_adult_patients_hospitalized_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.7399514
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.7396153
previous_day_admission_adult_covid_confirmed	percent_of_inpatients_with_covid_coverage	0.7395530
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7377828
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7375015
total_adult_patients_hospitalized_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.7368450
total_adult_patients_hospitalized_confirmed_covid	inpatient_beds_utilization_coverage	0.7354438
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7353820
total_adult_patients_hospitalized_confirmed_covid	inpatient_bed_covid_utilization_coverage	0.7352058
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_confirmed	0.7334666
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7322857
total_adult_patients_hospitalized_confirmed_covid	percent_of_inpatients_with_covid_coverage	0.7321614
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7307219
total_adult_patients_hospitalized_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.7303875
inpatient_beds_used_covid	previous_day_admission_adult_covid_suspected	0.7293198
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7286103
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid	0.7283919
previous_day_admission_adult_covid_suspected	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.7237105
previous_day_admission_adult_covid_suspected	staffed_icu_adult_patients_confirmed_covid	0.7154564
previous_day_admission_pediatric_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.6940496
inpatient_beds_used_covid	previous_day_admission_pediatric_covid_confirmed	0.6935931
previous_day_admission_adult_covid_confirmed	previous_day_admission_adult_covid_suspected	0.6933878
previous_day_admission_adult_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_covid	0.6927177
previous_day_admission_pediatric_covid_confirmed	staffed_icu_adult_patients_confirmed_covid	0.6912149
previous_day_admission_pediatric_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.6811709
previous_day_admission_adult_covid_suspected	total_adult_patients_hospitalized_confirmed_covid	0.6786911
previous_day_admission_pediatric_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid	0.6738767
previous_day_admission_adult_covid_confirmed	previous_day_admission_pediatric_covid_confirmed	0.6694631
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.6639125
staffed_adult_icu_bed_occupancy	total_pediatric_patients_hospitalized_confirmed_covid	0.6499389
inpatient_beds_used	total_pediatric_patients_hospitalized_confirmed_covid	0.6410542
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6371127
total_pediatric_patients_hospitalized_confirmed_covid	total_staffed_adult_icu_beds	0.6367354
total_pediatric_patients_hospitalized_confirmed_covid	percent_of_inpatients_with_covid_coverage	0.6304031
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6288550
total_pediatric_patients_hospitalized_confirmed_covid	inpatient_bed_covid_utilization_coverage	0.6286847
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6276407
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6276303
inpatient_beds	total_pediatric_patients_hospitalized_confirmed_covid	0.6270587
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6269541
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6268030
total_pediatric_patients_hospitalized_confirmed_covid	inpatient_beds_utilization_coverage	0.6267541
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6263187
total_pediatric_patients_hospitalized_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.6261862
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6201931
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6198864
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6190294
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6186096
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6177797
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6173310
total_pediatric_patients_hospitalized_confirmed_covid	total_staffed_adult_icu_beds_coverage	0.6159562
previous_day_admission_pediatric_covid_confirmed	staffed_adult_icu_bed_occupancy	0.6156846
total_pediatric_patients_hospitalized_confirmed_covid	adult_icu_bed_utilization_coverage	0.6152711
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid	0.6150925
total_pediatric_patients_hospitalized_confirmed_covid	adult_icu_bed_covid_utilization_coverage	0.6122794
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_confirmed	0.6040148
inpatient_beds_used_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.6023420
inpatient_beds_used	previous_day_admission_pediatric_covid_confirmed	0.6005205
previous_day_admission_pediatric_covid_confirmed	previous_day_admission_pediatric_covid_confirmed_coverage	0.5992945
previous_day_admission_pediatric_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid_coverage	0.5991465
previous_day_admission_pediatric_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.5990110
inpatient_beds	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5987599
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_confirmed	0.5971599
previous_day_admission_pediatric_covid_confirmed	inpatient_bed_covid_utilization_coverage	0.5962897
previous_day_admission_pediatric_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.5954770
previous_day_admission_pediatric_covid_confirmed	previous_day_admission_pediatric_covid_suspected_coverage	0.5952405
inpatient_beds_coverage	previous_day_admission_pediatric_covid_confirmed	0.5948192
previous_day_admission_pediatric_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.5947437
previous_day_admission_pediatric_covid_confirmed	percent_of_inpatients_with_covid_coverage	0.5946836
previous_day_admission_pediatric_covid_confirmed	inpatient_beds_utilization_coverage	0.5946157
previous_day_admission_pediatric_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.5944804
previous_day_admission_pediatric_covid_confirmed	total_staffed_adult_icu_beds	0.5941915
previous_day_admission_pediatric_covid_confirmed	staffed_icu_adult_patients_confirmed_covid_coverage	0.5940252
previous_day_admission_pediatric_covid_confirmed	staffed_adult_icu_bed_occupancy_coverage	0.5935406
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_confirmed	0.5935041
previous_day_admission_pediatric_covid_confirmed	adult_icu_bed_utilization_coverage	0.5930828
previous_day_admission_pediatric_covid_confirmed	total_staffed_adult_icu_beds_coverage	0.5926863
previous_day_admission_pediatric_covid_confirmed	adult_icu_bed_covid_utilization_coverage	0.5923265
inpatient_beds	previous_day_admission_pediatric_covid_confirmed	0.5887652
previous_day_admission_adult_covid_suspected	total_pediatric_patients_hospitalized_confirmed_covid	0.5870998
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_confirmed	0.5866771
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_confirmed	0.5846302
previous_day_admission_pediatric_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_covid	0.5844847
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5774897
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5746839
inpatient_beds_used	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5639578
total_adult_patients_hospitalized_confirmed_covid	inpatient_bed_covid_utilization	0.5636324
previous_day_admission_adult_covid_confirmed	inpatient_bed_covid_utilization	0.5623787
inpatient_beds_used_covid	inpatient_bed_covid_utilization	0.5615764
total_adult_patients_hospitalized_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5584400
total_adult_patients_hospitalized_confirmed_and_suspected_covid	inpatient_bed_covid_utilization	0.5574348
staffed_icu_adult_patients_confirmed_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5573659
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	total_staffed_adult_icu_beds	0.5453404
staffed_icu_adult_patients_confirmed_covid	inpatient_bed_covid_utilization	0.5420582
staffed_adult_icu_bed_occupancy	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5393169
previous_day_admission_adult_covid_confirmed	percent_of_inpatients_with_covid	0.5304352
staffed_icu_adult_patients_confirmed_and_suspected_covid	inpatient_bed_covid_utilization	0.5297375
total_adult_patients_hospitalized_confirmed_covid	percent_of_inpatients_with_covid	0.5295259
inpatient_beds_used_covid	percent_of_inpatients_with_covid	0.5274467
total_adult_patients_hospitalized_confirmed_and_suspected_covid	percent_of_inpatients_with_covid	0.5225242
previous_day_admission_adult_covid_suspected	previous_day_admission_pediatric_covid_confirmed	0.5154402
staffed_icu_adult_patients_confirmed_covid	percent_of_inpatients_with_covid	0.5102073
previous_day_admission_adult_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.5033674
staffed_icu_adult_patients_confirmed_and_suspected_covid	percent_of_inpatients_with_covid	0.4987789
previous_day_admission_adult_covid_suspected	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4971297
previous_day_admission_pediatric_covid_suspected	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.4961025
previous_day_admission_pediatric_covid_suspected	staffed_adult_icu_bed_occupancy_coverage	0.4958692
previous_day_admission_pediatric_covid_suspected	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.4957007
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected	0.4946810
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_suspected	0.4944403
previous_day_admission_pediatric_covid_suspected	inpatient_bed_covid_utilization_coverage	0.4943078
previous_day_admission_pediatric_covid_suspected	percent_of_inpatients_with_covid_coverage	0.4941986
previous_day_admission_pediatric_covid_suspected	total_adult_patients_hospitalized_confirmed_covid_coverage	0.4940229
previous_day_admission_pediatric_covid_suspected	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.4939834
previous_day_admission_pediatric_covid_suspected	inpatient_beds_utilization_coverage	0.4930823
previous_day_admission_pediatric_covid_suspected	total_staffed_adult_icu_beds_coverage	0.4930379
previous_day_admission_pediatric_covid_suspected	adult_icu_bed_covid_utilization_coverage	0.4927216
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_suspected	0.4927170
previous_day_admission_pediatric_covid_suspected	adult_icu_bed_utilization_coverage	0.4927168
previous_day_admission_pediatric_covid_suspected	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.4926956
previous_day_admission_pediatric_covid_suspected	staffed_icu_adult_patients_confirmed_covid_coverage	0.4926365
inpatient_beds_coverage	previous_day_admission_pediatric_covid_suspected	0.4921394
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_suspected	0.4897129
previous_day_admission_pediatric_covid_suspected	total_staffed_adult_icu_beds	0.4891424
staffed_icu_adult_patients_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization	0.4884347
previous_day_admission_pediatric_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected	0.4881135
staffed_icu_adult_patients_confirmed_covid	adult_icu_bed_covid_utilization	0.4878442
previous_day_admission_pediatric_covid_suspected	previous_day_admission_pediatric_covid_suspected_coverage	0.4873479
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_suspected	0.4830579
previous_day_admission_adult_covid_suspected	previous_day_admission_pediatric_covid_suspected	0.4824502
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4819701
previous_day_admission_pediatric_covid_suspected	staffed_adult_icu_bed_occupancy	0.4792360
previous_day_admission_adult_covid_confirmed	adult_icu_bed_covid_utilization	0.4775790
inpatient_beds_used	previous_day_admission_pediatric_covid_suspected	0.4760610
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	percent_of_inpatients_with_covid_coverage	0.4730860
inpatient_beds	previous_day_admission_pediatric_covid_suspected	0.4729263
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	inpatient_bed_covid_utilization_coverage	0.4724250
total_adult_patients_hospitalized_confirmed_covid	adult_icu_bed_covid_utilization	0.4718992
previous_day_admission_pediatric_covid_confirmed	previous_day_admission_pediatric_covid_suspected	0.4718283
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4713127
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4712987
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4709501
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.4704987
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4702586
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	inpatient_beds_utilization_coverage	0.4700052
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.4693301
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4647554
inpatient_beds_used_covid	adult_icu_bed_covid_utilization	0.4647158
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4646866
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4646714
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4626598
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4615425
total_adult_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization	0.4604509
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4597467
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4584093
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4569169
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	total_staffed_adult_icu_beds_coverage	0.4568395
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_utilization_coverage	0.4563310
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization_coverage	0.4533770
previous_day_admission_pediatric_covid_confirmed	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.4497657
previous_day_admission_pediatric_covid_suspected	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.4405507
previous_day_admission_pediatric_covid_suspected	staffed_icu_adult_patients_confirmed_covid	0.4257087
previous_day_admission_adult_covid_confirmed	previous_day_admission_pediatric_covid_suspected	0.4189704
previous_day_admission_pediatric_covid_suspected	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.4165718
inpatient_beds_used_covid	previous_day_admission_pediatric_covid_suspected	0.4165409
previous_day_admission_pediatric_covid_suspected	total_adult_patients_hospitalized_confirmed_covid	0.3942364
inpatient_beds_utilization	inpatient_bed_covid_utilization	0.3779809
total_pediatric_patients_hospitalized_confirmed_covid	inpatient_bed_covid_utilization	0.3653924
previous_day_admission_pediatric_covid_confirmed	inpatient_bed_covid_utilization	0.3615489
previous_day_admission_pediatric_covid_suspected	total_pediatric_patients_hospitalized_confirmed_covid	0.3498555
total_pediatric_patients_hospitalized_confirmed_covid	percent_of_inpatients_with_covid	0.3469324
previous_day_admission_pediatric_covid_confirmed	percent_of_inpatients_with_covid	0.3369592
previous_day_admission_pediatric_covid_suspected	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.3268280
staffed_adult_icu_bed_occupancy	adult_icu_bed_utilization	0.3243616
previous_day_admission_pediatric_covid_confirmed	adult_icu_bed_covid_utilization	0.3233226
total_pediatric_patients_hospitalized_confirmed_covid	adult_icu_bed_covid_utilization	0.3171752
date	inpatient_bed_covid_utilization	0.3153806
date	percent_of_inpatients_with_covid	0.3098482
staffed_adult_icu_bed_occupancy	inpatient_bed_covid_utilization	0.3000085
previous_day_admission_adult_covid_suspected	inpatient_bed_covid_utilization	0.2930097
adult_icu_bed_covid_utilization	adult_icu_bed_covid_utilization_coverage	0.2876082
adult_icu_bed_covid_utilization	adult_icu_bed_utilization_coverage	0.2875173
total_staffed_adult_icu_beds_coverage	adult_icu_bed_covid_utilization	0.2851898
inpatient_bed_covid_utilization	adult_icu_bed_utilization_coverage	0.2847900
inpatient_bed_covid_utilization	adult_icu_bed_covid_utilization_coverage	0.2829520
total_staffed_adult_icu_beds_coverage	inpatient_bed_covid_utilization	0.2816992
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_covid_utilization	0.2808244
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_covid_utilization	0.2804506
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_covid_utilization	0.2803295
staffed_adult_icu_bed_occupancy_coverage	inpatient_bed_covid_utilization	0.2782955
percent_of_inpatients_with_covid	adult_icu_bed_utilization_coverage	0.2767768
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_bed_covid_utilization	0.2756738
percent_of_inpatients_with_covid	adult_icu_bed_covid_utilization_coverage	0.2746931
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_bed_covid_utilization	0.2742286
total_staffed_adult_icu_beds_coverage	percent_of_inpatients_with_covid	0.2737468
staffed_adult_icu_bed_occupancy_coverage	percent_of_inpatients_with_covid	0.2700082
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_bed_covid_utilization	0.2694894
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization	0.2692132
hospital_onset_covid_coverage	adult_icu_bed_covid_utilization	0.2688147
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization	0.2687364
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_covid_utilization	0.2687356
date	adult_icu_bed_covid_utilization	0.2680821
previous_day_admission_pediatric_covid_confirmed_coverage	percent_of_inpatients_with_covid	0.2669369
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization	0.2668119
previous_day_admission_pediatric_covid_suspected_coverage	percent_of_inpatients_with_covid	0.2658410
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization	0.2657865
staffed_adult_icu_bed_occupancy	percent_of_inpatients_with_covid	0.2650966
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization	0.2649295
hospital_onset_covid_coverage	inpatient_bed_covid_utilization	0.2645687
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization	0.2642643
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization	0.2632987
inpatient_beds_utilization_coverage	adult_icu_bed_covid_utilization	0.2630888
inpatient_beds_coverage	adult_icu_bed_covid_utilization	0.2629031
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization	0.2626190
inpatient_bed_covid_utilization_coverage	adult_icu_bed_covid_utilization	0.2624158
inpatient_beds_utilization_coverage	inpatient_bed_covid_utilization	0.2615702
inpatient_beds_coverage	inpatient_bed_covid_utilization	0.2613264
inpatient_beds_used	inpatient_beds_utilization	0.2602224
total_staffed_adult_icu_beds	inpatient_bed_covid_utilization	0.2600229
staffed_icu_adult_patients_confirmed_covid_coverage	percent_of_inpatients_with_covid	0.2599662
previous_day_admission_adult_covid_suspected	inpatient_beds_utilization	0.2592159
inpatient_beds_used_coverage	adult_icu_bed_covid_utilization	0.2588010
percent_of_inpatients_with_covid_coverage	adult_icu_bed_covid_utilization	0.2585652
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization	0.2583494
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization	0.2574010
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_covid_utilization	0.2570598
inpatient_beds_used_coverage	inpatient_bed_covid_utilization	0.2570408
inpatient_beds_used_covid	inpatient_beds_utilization	0.2567911
total_adult_patients_hospitalized_confirmed_and_suspected_covid	inpatient_beds_utilization	0.2565926
hospital_onset_covid_coverage	percent_of_inpatients_with_covid	0.2565720
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid	0.2564516
inpatient_bed_covid_utilization	inpatient_bed_covid_utilization_coverage	0.2562489
previous_day_admission_adult_covid_suspected	percent_of_inpatients_with_covid	0.2555683
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_covid_utilization	0.2551006
previous_day_admission_adult_covid_confirmed_coverage	inpatient_bed_covid_utilization	0.2545827
total_adult_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid	0.2542791
total_pediatric_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid	0.2536402
inpatient_beds_used_covid_coverage	adult_icu_bed_covid_utilization	0.2531692
previous_day_admission_adult_covid_confirmed	inpatient_beds_utilization	0.2530957
inpatient_beds_utilization_coverage	percent_of_inpatients_with_covid	0.2529284
inpatient_beds_coverage	percent_of_inpatients_with_covid	0.2529248
percent_of_inpatients_with_covid_coverage	inpatient_bed_covid_utilization	0.2525784
inpatient_beds_used	inpatient_bed_covid_utilization	0.2516512
previous_day_admission_adult_covid_suspected	adult_icu_bed_covid_utilization	0.2515301
previous_day_admission_adult_covid_suspected_coverage	inpatient_bed_covid_utilization	0.2515029
inpatient_beds_used_covid_coverage	inpatient_bed_covid_utilization	0.2494863
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid	0.2494438
inpatient_beds_used_coverage	percent_of_inpatients_with_covid	0.2481581
total_adult_patients_hospitalized_confirmed_covid	inpatient_beds_utilization	0.2481147
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid	0.2480662
percent_of_inpatients_with_covid	inpatient_bed_covid_utilization_coverage	0.2475723
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	percent_of_inpatients_with_covid	0.2465049
previous_day_admission_adult_covid_confirmed_coverage	percent_of_inpatients_with_covid	0.2443906
staffed_adult_icu_bed_occupancy	adult_icu_bed_covid_utilization	0.2442570
percent_of_inpatients_with_covid	percent_of_inpatients_with_covid_coverage	0.2436570
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	inpatient_bed_covid_utilization	0.2431502
inpatient_beds_utilization	adult_icu_bed_covid_utilization	0.2426164
previous_day_admission_adult_covid_suspected_coverage	percent_of_inpatients_with_covid	0.2417158
inpatient_beds_used_covid_coverage	percent_of_inpatients_with_covid	0.2397827
staffed_icu_adult_patients_confirmed_covid	inpatient_beds_utilization	0.2394050
staffed_icu_adult_patients_confirmed_and_suspected_covid	inpatient_beds_utilization	0.2367526
staffed_adult_icu_bed_occupancy	inpatient_beds_utilization	0.2359616
total_staffed_adult_icu_beds	percent_of_inpatients_with_covid	0.2291261
inpatient_beds	inpatient_bed_covid_utilization	0.2253736
date	previous_day_admission_adult_covid_confirmed	0.2226129
total_staffed_adult_icu_beds	inpatient_beds_utilization	0.2208156
inpatient_beds_utilization	percent_of_inpatients_with_covid	0.2160565
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_covid_utilization	0.2144374
inpatient_beds_used	percent_of_inpatients_with_covid	0.2117081
date	total_adult_patients_hospitalized_confirmed_covid	0.2115224
inpatient_beds	percent_of_inpatients_with_covid	0.1991299
inpatient_beds	inpatient_beds_utilization	0.1968316
date	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.1857896
total_staffed_adult_icu_beds	adult_icu_bed_covid_utilization	0.1847884
inpatient_beds_used	adult_icu_bed_covid_utilization	0.1846472
previous_day_admission_pediatric_covid_confirmed	inpatient_beds_utilization	0.1838811
total_pediatric_patients_hospitalized_confirmed_covid	inpatient_beds_utilization	0.1828839
previous_day_admission_pediatric_covid_suspected	inpatient_bed_covid_utilization	0.1747457
date	staffed_icu_adult_patients_confirmed_covid	0.1711913
inpatient_beds	adult_icu_bed_covid_utilization	0.1686747
previous_day_admission_pediatric_covid_suspected	inpatient_beds_utilization	0.1635090
date	inpatient_beds_used_covid	0.1628343
previous_day_admission_pediatric_covid_suspected	percent_of_inpatients_with_covid	0.1535993
date	adult_icu_bed_utilization_coverage	0.1531091
date	adult_icu_bed_covid_utilization_coverage	0.1514842
date	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.1491255
inpatient_beds_utilization	adult_icu_bed_utilization_coverage	0.1458182
inpatient_beds_utilization	adult_icu_bed_covid_utilization_coverage	0.1454730
date	total_staffed_adult_icu_beds_coverage	0.1452204
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_beds_utilization	0.1450868
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization	0.1440653
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization	0.1439696
total_staffed_adult_icu_beds_coverage	inpatient_beds_utilization	0.1439183
staffed_adult_icu_bed_occupancy_coverage	inpatient_beds_utilization	0.1434257
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_beds_utilization	0.1422282
previous_day_admission_adult_covid_confirmed_coverage	inpatient_beds_utilization	0.1412323
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_beds_utilization	0.1404080
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization	0.1399584
previous_day_admission_adult_covid_suspected_coverage	inpatient_beds_utilization	0.1390847
previous_day_admission_pediatric_covid_suspected	adult_icu_bed_covid_utilization	0.1388505
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization	0.1385679
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization	0.1367993
inpatient_beds_used_covid_coverage	inpatient_beds_utilization	0.1365847
date	staffed_adult_icu_bed_occupancy_coverage	0.1361892
date	previous_day_admission_pediatric_covid_confirmed_coverage	0.1356750
inpatient_beds_utilization	inpatient_beds_utilization_coverage	0.1350572
inpatient_beds_used_coverage	inpatient_beds_utilization	0.1339832
inpatient_beds_coverage	inpatient_beds_utilization	0.1336687
inpatient_beds_utilization	inpatient_bed_covid_utilization_coverage	0.1335797
date	previous_day_admission_pediatric_covid_suspected_coverage	0.1334643
inpatient_beds_utilization	percent_of_inpatients_with_covid_coverage	0.1332050
adult_icu_bed_covid_utilization	adult_icu_bed_utilization	0.1331583
date	inpatient_beds_utilization	0.1302809
hospital_onset_covid_coverage	inpatient_beds_utilization	0.1299966
hospital_onset_covid	staffed_icu_adult_patients_confirmed_covid	0.1195126
hospital_onset_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.1193691
hospital_onset_covid	inpatient_beds_used_covid	0.1186751
hospital_onset_covid	previous_day_admission_pediatric_covid_confirmed_coverage	0.1181454
hospital_onset_covid	previous_day_admission_pediatric_covid_suspected_coverage	0.1178132
hospital_onset_covid	adult_icu_bed_covid_utilization_coverage	0.1177394
hospital_onset_covid	adult_icu_bed_utilization_coverage	0.1174075
hospital_onset_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.1173634
hospital_onset_covid	staffed_adult_icu_bed_occupancy_coverage	0.1172987
hospital_onset_covid	total_staffed_adult_icu_beds_coverage	0.1172902
hospital_onset_covid	hospital_onset_covid_coverage	0.1170734
hospital_onset_covid	total_adult_patients_hospitalized_confirmed_covid	0.1169033
hospital_onset_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.1167430
hospital_onset_covid	staffed_icu_adult_patients_confirmed_covid_coverage	0.1167271
hospital_onset_covid	previous_day_admission_adult_covid_confirmed	0.1165360
hospital_onset_covid	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.1164993
hospital_onset_covid	inpatient_bed_covid_utilization_coverage	0.1162598
hospital_onset_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.1162491
hospital_onset_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.1158689
hospital_onset_covid	total_adult_patients_hospitalized_confirmed_covid_coverage	0.1158665
hospital_onset_covid	percent_of_inpatients_with_covid_coverage	0.1158417
hospital_onset_covid	inpatient_beds_coverage	0.1157416
hospital_onset_covid	inpatient_beds_utilization_coverage	0.1157103
hospital_onset_covid	inpatient_beds_used_coverage	0.1153978
hospital_onset_covid	previous_day_admission_adult_covid_suspected_coverage	0.1153938
hospital_onset_covid	inpatient_beds_used_covid_coverage	0.1152968
hospital_onset_covid	previous_day_admission_adult_covid_confirmed_coverage	0.1152270
inpatient_bed_covid_utilization	adult_icu_bed_utilization	0.1132477
date	staffed_icu_adult_patients_confirmed_covid_coverage	0.1091037
hospital_onset_covid	staffed_adult_icu_bed_occupancy	0.1076485
hospital_onset_covid	inpatient_beds_used	0.1073296
hospital_onset_covid	inpatient_beds	0.1054746
inpatient_beds_utilization	adult_icu_bed_utilization	0.1049507
date	previous_day_admission_pediatric_covid_confirmed	0.1034073
hospital_onset_covid	total_staffed_adult_icu_beds	0.1032130
date	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.1030429
percent_of_inpatients_with_covid	adult_icu_bed_utilization	0.1009193
date	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.0984555
date	staffed_adult_icu_bed_occupancy	0.0980999
hospital_onset_covid	total_pediatric_patients_hospitalized_confirmed_covid	0.0980179
date	previous_day_admission_adult_covid_confirmed_coverage	0.0928689
hospital_onset_covid	previous_day_admission_pediatric_covid_confirmed	0.0918186
date	previous_day_admission_adult_covid_suspected_coverage	0.0918078
hospital_onset_covid	previous_day_admission_adult_covid_suspected	0.0916476
date	total_adult_patients_hospitalized_confirmed_covid_coverage	0.0913110
date	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.0907434
date	hospital_onset_covid_coverage	0.0854448
date	total_staffed_adult_icu_beds	0.0845509
hospital_onset_covid	previous_day_admission_pediatric_covid_suspected	0.0831615
date	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.0810695
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	inpatient_beds_utilization	0.0800650
staffed_icu_adult_patients_confirmed_covid	adult_icu_bed_utilization	0.0797428
staffed_icu_adult_patients_confirmed_and_suspected_covid	adult_icu_bed_utilization	0.0790008
hospital_onset_covid	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	0.0778526
date	inpatient_bed_covid_utilization_coverage	0.0768398
date	inpatient_beds_utilization_coverage	0.0767919
previous_day_admission_adult_covid_confirmed	adult_icu_bed_utilization	0.0759952
adult_icu_bed_utilization	adult_icu_bed_utilization_coverage	0.0757540
adult_icu_bed_covid_utilization_coverage	adult_icu_bed_utilization	0.0756524
total_staffed_adult_icu_beds_coverage	adult_icu_bed_utilization	0.0752008
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_utilization	0.0748508
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_utilization	0.0747575
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_utilization	0.0746704
total_adult_patients_hospitalized_confirmed_covid	adult_icu_bed_utilization	0.0738299
date	inpatient_beds_coverage	0.0733711
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization	0.0730689
inpatient_beds_used_covid	adult_icu_bed_utilization	0.0728554
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization	0.0724930
total_adult_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_utilization	0.0723034
hospital_onset_covid_coverage	adult_icu_bed_utilization	0.0722429
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization	0.0721186
inpatient_bed_covid_utilization_coverage	adult_icu_bed_utilization	0.0721107
inpatient_beds_utilization_coverage	adult_icu_bed_utilization	0.0719389
percent_of_inpatients_with_covid_coverage	adult_icu_bed_utilization	0.0718243
inpatient_beds_coverage	adult_icu_bed_utilization	0.0717514
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_utilization	0.0716463
inpatient_beds_used_coverage	adult_icu_bed_utilization	0.0714188
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization	0.0712090
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization	0.0711061
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_utilization	0.0710901
date	percent_of_inpatients_with_covid_coverage	0.0710836
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_utilization	0.0710518
inpatient_beds_used_covid_coverage	adult_icu_bed_utilization	0.0691635
date	inpatient_beds_used	0.0677232
date	inpatient_beds_used_coverage	0.0664608
hospital_onset_covid	inpatient_bed_covid_utilization	0.0631746
previous_day_admission_pediatric_covid_confirmed	adult_icu_bed_utilization	0.0610110
hospital_onset_covid	percent_of_inpatients_with_covid	0.0598627
hospital_onset_covid	adult_icu_bed_covid_utilization	0.0580074
date	previous_day_admission_pediatric_covid_suspected	0.0552790
inpatient_beds_used	adult_icu_bed_utilization	0.0548077
total_pediatric_patients_hospitalized_confirmed_covid	adult_icu_bed_utilization	0.0543952
date	inpatient_beds	0.0504816
inpatient_beds	adult_icu_bed_utilization	0.0502217
date	total_pediatric_patients_hospitalized_confirmed_covid	0.0491152
previous_day_admission_adult_covid_suspected	adult_icu_bed_utilization	0.0478916
total_staffed_adult_icu_beds	adult_icu_bed_utilization	0.0474861
previous_day_admission_pediatric_covid_suspected	adult_icu_bed_utilization	0.0432471
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	adult_icu_bed_utilization	0.0401633
date	inpatient_beds_used_covid_coverage	0.0397630
date	adult_icu_bed_utilization	0.0329270
hospital_onset_covid	inpatient_beds_utilization	0.0317347
date	hospital_onset_covid	0.0189482
state	hospital_onset_covid	0.0164736
hospital_onset_covid	adult_icu_bed_utilization	0.0088412
state	previous_day_admission_pediatric_covid_suspected	0.0016594
state	date	-0.0028777
state	total_staffed_adult_icu_beds_coverage	-0.0290390
state	staffed_adult_icu_bed_occupancy_coverage	-0.0299497
state	adult_icu_bed_utilization_coverage	-0.0302938
date	previous_day_admission_adult_covid_suspected	-0.0323004
state	adult_icu_bed_covid_utilization_coverage	-0.0326394
date	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	-0.0380640
state	inpatient_beds_coverage	-0.0396058
state	percent_of_inpatients_with_covid_coverage	-0.0399361
state	inpatient_beds_utilization_coverage	-0.0401825
state	inpatient_beds_used_coverage	-0.0407960
state	staffed_icu_adult_patients_confirmed_covid_coverage	-0.0409426
state	inpatient_bed_covid_utilization_coverage	-0.0413760
state	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	-0.0416511
state	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	-0.0420968
state	total_pediatric_patients_hospitalized_confirmed_covid_coverage	-0.0427395
state	previous_day_admission_pediatric_covid_confirmed_coverage	-0.0428123
state	total_adult_patients_hospitalized_confirmed_covid_coverage	-0.0441769
state	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	-0.0442975
state	previous_day_admission_pediatric_covid_suspected_coverage	-0.0444209
state	previous_day_admission_adult_covid_confirmed_coverage	-0.0451595
state	previous_day_admission_adult_covid_suspected_coverage	-0.0451716
state	hospital_onset_covid_coverage	-0.0452435
state	inpatient_beds_used_covid_coverage	-0.0460343
state	adult_icu_bed_utilization	-0.0472145
state	total_pediatric_patients_hospitalized_confirmed_covid	-0.0747969
state	previous_day_admission_pediatric_covid_confirmed	-0.0788183
state	inpatient_beds_used	-0.0851861
state	inpatient_beds	-0.0859033
state	staffed_adult_icu_bed_occupancy	-0.0870157
state	total_staffed_adult_icu_beds	-0.0892811
state	total_adult_patients_hospitalized_confirmed_covid	-0.0900786
state	staffed_icu_adult_patients_confirmed_covid	-0.0914986
state	total_adult_patients_hospitalized_confirmed_and_suspected_covid	-0.0944692
state	percent_of_inpatients_with_covid	-0.0957743
state	previous_day_admission_adult_covid_confirmed	-0.0983298
state	staffed_icu_adult_patients_confirmed_and_suspected_covid	-0.0985965
state	inpatient_beds_used_covid	-0.0990943
state	previous_day_admission_adult_covid_suspected	-0.1024433
state	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid	-0.1049748
state	inpatient_bed_covid_utilization	-0.1180212
state	adult_icu_bed_covid_utilization	-0.1262841
state	inpatient_beds_utilization	-0.1609090

From the results, I noticed that many of the predictors have near perfect collinearity. I filtered out predictor pairs with the absolute value of correlation coefficients above 0.90. The tibble containing all distinct predictor pairs with near perfect collinearity is printed below:

# explore collinearity
near_perfect_collinearity <- corr_pred %>% 
  filter(abs(correlation) > 0.90)

near_perfect_collinearity %>% 
  kbl() %>%
  kable_paper() %>% 
  scroll_box(width = "100%", height = "200px") %>% 
  kableExtra::footnote(general = 
                         "independent variable pairs with near perfect collinearity")

x	y	correlation
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9996887
inpatient_beds_used_coverage	inpatient_beds_utilization_coverage	0.9995873
total_staffed_adult_icu_beds_coverage	adult_icu_bed_utilization_coverage	0.9995520
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_utilization_coverage	0.9992595
staffed_adult_icu_bed_occupancy_coverage	total_staffed_adult_icu_beds_coverage	0.9991530
adult_icu_bed_covid_utilization_coverage	adult_icu_bed_utilization_coverage	0.9991155
inpatient_beds_coverage	inpatient_beds_utilization_coverage	0.9991039
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9991014
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9990155
total_staffed_adult_icu_beds_coverage	adult_icu_bed_covid_utilization_coverage	0.9989580
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9989385
percent_of_inpatients_with_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9988549
inpatient_beds_coverage	inpatient_beds_used_coverage	0.9986980
staffed_adult_icu_bed_occupancy_coverage	adult_icu_bed_covid_utilization_coverage	0.9982268
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9971256
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9970327
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9965775
total_adult_patients_hospitalized_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9962535
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9960787
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9959898
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9959042
staffed_icu_adult_patients_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_covid	0.9958744
previous_day_admission_pediatric_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9957961
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9957329
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9955322
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9953369
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9953174
inpatient_beds_used_coverage	percent_of_inpatients_with_covid_coverage	0.9952513
inpatient_beds_utilization_coverage	percent_of_inpatients_with_covid_coverage	0.9948947
inpatient_beds_coverage	inpatient_bed_covid_utilization_coverage	0.9948889
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9948749
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9948272
inpatient_beds_utilization_coverage	inpatient_bed_covid_utilization_coverage	0.9944642
hospital_onset_covid_coverage	inpatient_beds_coverage	0.9943271
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9941344
inpatient_beds_used_coverage	inpatient_bed_covid_utilization_coverage	0.9941095
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9940599
total_pediatric_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9940044
hospital_onset_covid_coverage	inpatient_beds_utilization_coverage	0.9939023
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9938344
inpatient_beds_used_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9938268
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9937893
inpatient_beds_coverage	percent_of_inpatients_with_covid_coverage	0.9937467
inpatient_beds_used_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9937332
previous_day_admission_adult_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9936703
total_adult_patients_hospitalized_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9936323
hospital_onset_covid_coverage	inpatient_beds_used_coverage	0.9935837
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9934683
previous_day_admission_pediatric_covid_suspected_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9933185
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9932943
previous_day_admission_adult_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9932664
inpatient_beds_used_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9932300
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9931901
inpatient_beds_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9931802
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9931158
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9928667
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9927745
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9927368
staffed_icu_adult_patients_confirmed_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9926262
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9923912
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9921286
staffed_icu_adult_patients_confirmed_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9919042
inpatient_beds_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9918265
inpatient_beds_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9918234
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9917794
inpatient_beds_used_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9917270
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9917232
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9917030
previous_day_admission_adult_covid_confirmed_coverage	inpatient_beds_utilization_coverage	0.9916734
previous_day_admission_adult_covid_suspected_coverage	inpatient_beds_utilization_coverage	0.9916545
inpatient_beds_used_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9915721
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9915355
hospital_onset_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9915328
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9915288
inpatient_beds_used_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9914595
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9912689
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9911244
hospital_onset_covid_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9909643
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9909582
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9909015
hospital_onset_covid_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9908878
hospital_onset_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9908083
staffed_adult_icu_bed_occupancy_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9907483
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9907325
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9906539
hospital_onset_covid_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9905503
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9905158
inpatient_beds	inpatient_beds_used	0.9904805
inpatient_beds_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9904770
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	inpatient_beds_utilization_coverage	0.9904270
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9902753
inpatient_beds_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9902579
total_adult_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9902323
inpatient_beds_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9901904
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9901272
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9900715
staffed_icu_adult_patients_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9900656
total_pediatric_patients_hospitalized_confirmed_covid_coverage	inpatient_beds_utilization_coverage	0.9900138
previous_day_admission_adult_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9899790
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_covid	0.9899383
previous_day_admission_adult_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9898924
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9898156
inpatient_beds_used_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9897731
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9897448
hospital_onset_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9897429
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9897391
staffed_adult_icu_bed_occupancy_coverage	inpatient_beds_utilization_coverage	0.9897328
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9897189
inpatient_beds_used_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9897160
staffed_icu_adult_patients_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9896769
previous_day_admission_adult_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9896244
previous_day_admission_pediatric_covid_suspected_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9895801
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9895620
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9894987
previous_day_admission_adult_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9894330
inpatient_beds_used_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9893665
staffed_icu_adult_patients_confirmed_covid_coverage	inpatient_bed_covid_utilization_coverage	0.9893092
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_covid_utilization_coverage	0.9893031
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9891756
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_covid_utilization_coverage	0.9891555
previous_day_admission_pediatric_covid_confirmed_coverage	adult_icu_bed_utilization_coverage	0.9891549
previous_day_admission_pediatric_covid_suspected_coverage	adult_icu_bed_utilization_coverage	0.9891015
previous_day_admission_pediatric_covid_confirmed_coverage	total_staffed_adult_icu_beds_coverage	0.9890652
previous_day_admission_pediatric_covid_suspected_coverage	total_staffed_adult_icu_beds_coverage	0.9890076
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9888732
previous_day_admission_pediatric_covid_confirmed_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9888182
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9887556
inpatient_beds_used_coverage	inpatient_beds_used_covid_coverage	0.9887502
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9886461
previous_day_admission_pediatric_covid_suspected_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9884399
inpatient_beds_coverage	inpatient_beds_used_covid_coverage	0.9884179
hospital_onset_covid_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9884133
inpatient_beds_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9884107
inpatient_beds_coverage	total_staffed_adult_icu_beds_coverage	0.9883926
hospital_onset_covid_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9883211
previous_day_admission_adult_covid_suspected_coverage	inpatient_bed_covid_utilization_coverage	0.9882861
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_beds_utilization_coverage	0.9882223
inpatient_beds_used_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9881351
previous_day_admission_adult_covid_confirmed_coverage	inpatient_bed_covid_utilization_coverage	0.9881015
staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9878637
inpatient_beds_used_covid_coverage	inpatient_beds_utilization_coverage	0.9878376
total_staffed_adult_icu_beds_coverage	inpatient_beds_utilization_coverage	0.9878079
previous_day_admission_adult_covid_suspected_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9877358
previous_day_admission_adult_covid_confirmed_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9875735
staffed_icu_adult_patients_confirmed_covid_coverage	percent_of_inpatients_with_covid_coverage	0.9874270
previous_day_admission_adult_covid_suspected_coverage	percent_of_inpatients_with_covid_coverage	0.9874260
previous_day_admission_adult_covid_suspected_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9873919
previous_day_admission_adult_covid_confirmed_coverage	percent_of_inpatients_with_covid_coverage	0.9873715
previous_day_admission_adult_covid_confirmed_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9871433
inpatient_beds_coverage	adult_icu_bed_utilization_coverage	0.9869770
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9869622
staffed_adult_icu_bed_occupancy_coverage	inpatient_bed_covid_utilization_coverage	0.9866998
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9866746
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9865912
inpatient_beds_utilization_coverage	adult_icu_bed_utilization_coverage	0.9865560
staffed_adult_icu_bed_occupancy_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9864739
hospital_onset_covid_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9864464
previous_day_admission_pediatric_covid_suspected_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9859720
inpatient_beds_coverage	adult_icu_bed_covid_utilization_coverage	0.9858677
inpatient_beds_utilization_coverage	adult_icu_bed_covid_utilization_coverage	0.9856891
inpatient_beds_used_coverage	total_staffed_adult_icu_beds_coverage	0.9855934
inpatient_beds_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9855601
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_beds_utilization_coverage	0.9854267
previous_day_admission_adult_covid_suspected_coverage	total_staffed_adult_icu_beds_coverage	0.9853724
hospital_onset_covid_coverage	inpatient_beds_used_covid_coverage	0.9852947
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9851906
previous_day_admission_pediatric_covid_suspected_coverage	inpatient_bed_covid_utilization_coverage	0.9851047
previous_day_admission_adult_covid_confirmed_coverage	total_staffed_adult_icu_beds_coverage	0.9850113
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_utilization_coverage	0.9847953
hospital_onset_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9847691
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_and_suspected_covid_coverage	0.9847645
staffed_adult_icu_bed_occupancy_coverage	percent_of_inpatients_with_covid_coverage	0.9847005
total_pediatric_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9845441
total_staffed_adult_icu_beds_coverage	inpatient_bed_covid_utilization_coverage	0.9845177
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_utilization_coverage	0.9844332
previous_day_admission_adult_covid_suspected_coverage	adult_icu_bed_covid_utilization_coverage	0.9843965
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9843849
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9843551
inpatient_beds_used_coverage	adult_icu_bed_utilization_coverage	0.9841352
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9840972
previous_day_admission_pediatric_covid_confirmed_coverage	total_pediatric_patients_hospitalized_confirmed_covid_coverage	0.9840833
total_pediatric_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9840409
staffed_adult_icu_bed_occupancy_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9840216
inpatient_beds_used_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9839811
previous_day_admission_adult_covid_confirmed_coverage	adult_icu_bed_covid_utilization_coverage	0.9837723
hospital_onset_covid_coverage	adult_icu_bed_utilization_coverage	0.9837721
inpatient_beds_used_covid_coverage	staffed_icu_adult_patients_confirmed_covid_coverage	0.9837460
total_adult_patients_hospitalized_confirmed_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9837270
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9837183
hospital_onset_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9836920
total_pediatric_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9835507
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_confirmed_coverage	0.9834334
inpatient_bed_covid_utilization_coverage	adult_icu_bed_utilization_coverage	0.9834001
inpatient_beds_used_covid_coverage	previous_day_admission_adult_covid_suspected_coverage	0.9831954
inpatient_beds_used_coverage	adult_icu_bed_covid_utilization_coverage	0.9831770
previous_day_admission_pediatric_covid_suspected_coverage	percent_of_inpatients_with_covid_coverage	0.9830427
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_covid_coverage	0.9830395
inpatient_bed_covid_utilization_coverage	adult_icu_bed_covid_utilization_coverage	0.9829885
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_utilization_coverage	0.9826923
previous_day_admission_pediatric_covid_confirmed_coverage	inpatient_bed_covid_utilization_coverage	0.9824130
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9823367
total_adult_patients_hospitalized_confirmed_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9823068
previous_day_admission_pediatric_covid_confirmed_coverage	total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	0.9820894
total_staffed_adult_icu_beds_coverage	percent_of_inpatients_with_covid_coverage	0.9818945
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_covid	0.9812115
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_utilization_coverage	0.9810497
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9810439
total_adult_patients_hospitalized_confirmed_and_suspected_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9808029
percent_of_inpatients_with_covid_coverage	adult_icu_bed_utilization_coverage	0.9806204
previous_day_admission_pediatric_covid_confirmed_coverage	percent_of_inpatients_with_covid_coverage	0.9804751
percent_of_inpatients_with_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9800667
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9788504
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_covid	0.9767366
inpatient_beds	total_staffed_adult_icu_beds	0.9763855
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9761728
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_suspected_coverage	0.9760262
percent_of_inpatients_with_covid	inpatient_bed_covid_utilization	0.9751065
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9747235
inpatient_beds_used	total_staffed_adult_icu_beds	0.9745122
inpatient_beds_used_covid_coverage	staffed_adult_icu_bed_occupancy_coverage	0.9727648
inpatient_beds_used_covid_coverage	previous_day_admission_pediatric_covid_confirmed_coverage	0.9726784
inpatient_beds_used_covid_coverage	total_staffed_adult_icu_beds_coverage	0.9696686
inpatient_beds_used_covid_coverage	adult_icu_bed_utilization_coverage	0.9676645
inpatient_beds_used_covid_coverage	adult_icu_bed_covid_utilization_coverage	0.9671422
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid	0.9641409
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9624642
inpatient_beds_used_covid	previous_day_admission_adult_covid_confirmed	0.9551771
staffed_adult_icu_bed_occupancy	total_staffed_adult_icu_beds	0.9490643
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_covid	0.9448888
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9409511
inpatient_beds_used	staffed_adult_icu_bed_occupancy	0.9367275
inpatient_beds	staffed_adult_icu_bed_occupancy	0.9311894

Note: independent variable pairs with near perfect collinearity

Shown by the resulting tibble after filtering, the many of the variable pairs with near perfect collinearity are between variables ending with _coverage. Checking the data dictionary, I learned that values of these variables represent the number of hospitals reporting the corresponding data in the state on the given date. Thus, it make sense for them to have a strong linear relation, since one hospital reporting one type of data is likely to also report other types of data at the same time. In fact, the different _coverage values are likely to be almost equal, shown by the example visualization between inpatient_beds_used_coverage and inpatient_beds_utilization_coverage:

# visualize relation btw different coverages
covid_data %>% 
  ggplot(aes(inpatient_beds_used_coverage, 
             inpatient_beds_utilization_coverage)) + 
  geom_point() + 
  geom_smooth(se = FALSE) + 
  labs(
    title = "Relation between Different Coverage Variables"
  )

In the plot, the diagonal fitted line confirms the near perfect collinearity.

To verify the near perfect collinearity between all _coverage variables, I created the correlation plot below for all variables in the dataset ending with _coverage using methods from the corrplot package. This plot provides a general view on the degrees of inter-variables correlations for all predictors in covid_data ending with _coverage instead of focusing on the correlation between any specific set of variables. Thus, I used indexed strings matching column position of each variable (X1, X2, etc.) as the temporary variable names in this plot, avoiding the spacing problem caused by long variable names.

# correlation plot between all numeric predictors
# vector for the temporary column names
temp_col_names <- 
  # indexed strings
  paste(c("X"), 1:21, sep="")

covid_data %>% 
  # select only numeric predictors
  select(ends_with("_coverage")) %>% 
  # temporarily rename all columns to indexed strings
  rename_all(~ temp_col_names) %>% 
  drop_na() %>% 
  # compute correlation matrix
  cor() %>% 
  # visualize
  corrplot(type = "upper", 
           title = "Correlations between Variables Ending with `_coverage`", 
           mar = c(0, 0, 1, 0))

As shown, the universally observed dark blue circles verifies the near perfect collinearity. I decided to remove predictor variables with near perfect collinearity to avoid potential problems in statistical learning and to simplify the dataset for the later process. I kept only inpatient_beds_coverage and removed all other predictor variables ending with _coverage:

covid_data <- covid_data %>% 
  # remove variables with near perfect collinearity
  # only keep `inpatient_beds_coverage`
  select(-c(ends_with("_coverage")), inpatient_beds_coverage)

After removing the redundant _coverage variables, I checked again for any remaining collinearity between predictor variables in the dataset:

# remaining strong collinearity
remain_near_perfect_collinearity <- covid_data %>% 
  # unselect outcome variable
  select(-c(critical_staffing_shortage_today_yes)) %>% 
  # temporarily change `state` and `date` to type numeric
  mutate(date = as.numeric(date),
         # first turn state into a factor
         # then turn it into a numeric variable
         # with values determined by factor levels
         state = as.numeric(as.factor(state))) %>%
  # remove rows with missing data
  drop_na() %>%
  # correlation matrix
  correlate() %>% 
  # turn into a tibble
  stretch() %>% 
  rename("correlation" = "r") %>% 
  # obtain rows with correlation greater than 0.90
  filter(correlation > 0.9) %>% 
  arrange(desc(correlation))

# show tibble
kbl(remain_near_perfect_collinearity) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "200px")

x	y	correlation
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9959898
total_adult_patients_hospitalized_confirmed_and_suspected_covid	inpatient_beds_used_covid	0.9959898
staffed_icu_adult_patients_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_covid	0.9958744
staffed_icu_adult_patients_confirmed_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9958744
total_adult_patients_hospitalized_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9957329
total_adult_patients_hospitalized_confirmed_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9957329
inpatient_beds	inpatient_beds_used	0.9904805
inpatient_beds_used	inpatient_beds	0.9904805
inpatient_beds_used_covid	total_adult_patients_hospitalized_confirmed_covid	0.9899383
total_adult_patients_hospitalized_confirmed_covid	inpatient_beds_used_covid	0.9899383
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_covid	0.9812115
total_adult_patients_hospitalized_confirmed_covid	staffed_icu_adult_patients_confirmed_covid	0.9812115
staffed_icu_adult_patients_confirmed_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9810439
total_adult_patients_hospitalized_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_covid	0.9810439
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9788504
total_adult_patients_hospitalized_confirmed_and_suspected_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9788504
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_covid	0.9767366
staffed_icu_adult_patients_confirmed_covid	inpatient_beds_used_covid	0.9767366
inpatient_beds	total_staffed_adult_icu_beds	0.9763855
total_staffed_adult_icu_beds	inpatient_beds	0.9763855
inpatient_beds_used_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9761728
staffed_icu_adult_patients_confirmed_and_suspected_covid	inpatient_beds_used_covid	0.9761728
percent_of_inpatients_with_covid	inpatient_bed_covid_utilization	0.9751065
inpatient_bed_covid_utilization	percent_of_inpatients_with_covid	0.9751065
staffed_icu_adult_patients_confirmed_and_suspected_covid	total_adult_patients_hospitalized_confirmed_covid	0.9747235
total_adult_patients_hospitalized_confirmed_covid	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9747235
inpatient_beds_used	total_staffed_adult_icu_beds	0.9745122
total_staffed_adult_icu_beds	inpatient_beds_used	0.9745122
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_covid	0.9641409
total_adult_patients_hospitalized_confirmed_covid	previous_day_admission_adult_covid_confirmed	0.9641409
previous_day_admission_adult_covid_confirmed	total_adult_patients_hospitalized_confirmed_and_suspected_covid	0.9624642
total_adult_patients_hospitalized_confirmed_and_suspected_covid	previous_day_admission_adult_covid_confirmed	0.9624642
inpatient_beds_used_covid	previous_day_admission_adult_covid_confirmed	0.9551771
previous_day_admission_adult_covid_confirmed	inpatient_beds_used_covid	0.9551771
staffed_adult_icu_bed_occupancy	total_staffed_adult_icu_beds	0.9490643
total_staffed_adult_icu_beds	staffed_adult_icu_bed_occupancy	0.9490643
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_covid	0.9448888
staffed_icu_adult_patients_confirmed_covid	previous_day_admission_adult_covid_confirmed	0.9448888
previous_day_admission_adult_covid_confirmed	staffed_icu_adult_patients_confirmed_and_suspected_covid	0.9409511
staffed_icu_adult_patients_confirmed_and_suspected_covid	previous_day_admission_adult_covid_confirmed	0.9409511
inpatient_beds_used	staffed_adult_icu_bed_occupancy	0.9367275
staffed_adult_icu_bed_occupancy	inpatient_beds_used	0.9367275
inpatient_beds	staffed_adult_icu_bed_occupancy	0.9311894
staffed_adult_icu_bed_occupancy	inpatient_beds	0.9311894

As shown, the remaining highly correlated predictor pairs are between variables starting with previous_ or total_ and between variables containing _confirmed_and_suspected or _confirmed.

Shown by the visualization below, the value of confirmed and suspected cases show strong collinearity with the number of confirmed cases:

# visualize inter-variable correlations between predictors
covid_data %>% 
  ggplot(aes(total_adult_patients_hospitalized_confirmed_covid, 
             total_adult_patients_hospitalized_confirmed_and_suspected_covid)) +
  geom_point() + 
  geom_smooth(se = FALSE) +
  labs(
    title =  "Relation Between Confirmed and Confirmed and Suspected Cases", 
    x = "Confirmed Cases", 
    y = "Confirmed and Suspected Cases"
  )

The collinearity makes sense, since for the same group of patients (i.e. adult or ICU patients), the number of confirmed COVID cases and the number of confirmed and suspected cases are likely to be linear combinations of each other.

Moreover, the total confirmed COVID cases for each patient group has a strong positive relation with the previous day confirmed COVID cases, since one can be computed from another.

For example, previous_day_admission_adult_covid_confirmed has a direct linear relation with total_adult_patients_hospitalized_confirmed_covid:

# visualize inter-variable correlations between predictors
covid_data %>% 
  ggplot(aes(previous_day_admission_adult_covid_confirmed, 
             total_adult_patients_hospitalized_confirmed_covid)) + 
  geom_point() + 
  geom_smooth(se = FALSE) +
  labs(
    title =  "Relation Between Previous Day and Total Confirmed Cases", 
    x = "Previous Day Confirmed Cases", 
    y = "Total Confirmed Cases"
  )

Also, since inpatient_beds_used_covid is the total number of patients currently hospitalized in an inpatient bed who have suspected or confirmed COVID-19 in this state, it is the linear combination of the numbers of all groups of hospitalized patients who have suspected or confirmed COVID-19. Thus, it covers the information regarding hospital_onset_covid (the total current inpatients with onset of suspected or laboratory-confirmed COVID-19 fourteen or more days after admission for a condition other than COVID-19), total_adult_patients_hospitalized_confirmed_and_suspected_covid (the reported patients currently hospitalized in an adult inpatient bed who have confirmed or suspected COVID-19), total_pediatric_patients_hospitalized_confirmed_and_suspected_covid (the reported patients currently hospitalized in a pediatric inpatient bed who are suspected or laboratory-confirmed-positive for COVID-19), and staffed_icu_adult_patients_confirmed_and_suspected_covid (the reported patients currently hospitalized in an adult ICU bed who have suspected or confirmed COVID-19).

For illustration of the relation, I presented the scatterplot for the relation between inpatient_beds_used_covid and the sum of total_adult_patients_hospitalized_confirmed_and_suspected_covid and total_pediatric_patients_hospitalized_confirmed_and_suspected_covid:

covid_data %>% 
  mutate(
    total_confirmed_and_suspected = 
      total_adult_patients_hospitalized_confirmed_and_suspected_covid + 
      total_pediatric_patients_hospitalized_confirmed_and_suspected_covid
  ) %>% 
  ggplot(aes(inpatient_beds_used_covid, 
             total_confirmed_and_suspected)) +
  geom_point() + 
  geom_smooth(se = FALSE) + 
  labs(
    title =  "Inpatient Bed Usage and Confirmed and Suspected Cases", 
    x = "Inpatient Bed Usage Related to COVID", 
    y = "Confirmed and Suspected Cases"
  )

Thus, I decided to only keep variable inpatient_beds_used_covid as the holistic representation of the conditions of hospital usage related to COVID-19 and remove other redundant columns (variables containing _covid):

# remove redundant predictors
covid_data <- covid_data %>% 
  select(-contains("_covid"), inpatient_beds_used_covid)

Also, inpatient_beds is highly correlated with inpatient_beds_used, staffed_adult_icu_bed_occupancy, and total_staffed_adult_icu_beds:

# visualize inter-variable correlations between predictors
covid_data %>% 
  ggplot(aes(inpatient_beds, 
             inpatient_beds_used)) +
  geom_point() + 
  geom_smooth(se = FALSE) + 
  labs(
    title =  "Relation Between Total and Used Inpatient Beds", 
    x = "Total Inpatient Beds", 
    y = "Used Inpatient Beds"
  )

covid_data %>% 
  ggplot(aes(inpatient_beds, 
             total_staffed_adult_icu_beds)) +
  geom_point() + 
  geom_smooth(se = FALSE) + 
  labs(
    title =  "Relation Between Total Inpatient Beds and ICU Beds", 
    x = "Total Inpatient Beds", 
    y = "Staffed ICU Beds"
  ) + 
  xlim(0, 75000)

The high correlation makes sense, since inpatient_beds, inpatient_beds_used, staffed_adult_icu_bed_occupancy, and total_staffed_adult_icu_beds all convey information about the general hospital resource capacity for a specific state at a given date. inpatient_beds (the reported total number of staffed inpatient beds including all overflow and surge/expansion beds used for inpatients (includes all ICU beds)) covers the information contained in total_staffed_adult_icu_beds. Moreover, the number of inpatient bed usage is related to the overall capacity of the hospital system. States with greater capacity has higher number of inpatient_beds, and they can admit more patients, leading to a higher number of inpatient_beds_used. Based on the observation, I kept variable inpatient_beds as an indicator of the overall hospital resource capacity in a state on a given date, and I removed the other variables having near perfect collinearity with inpatient_beds:

# remove redundant predictors
covid_data <- covid_data %>% 
  select(-c(`inpatient_beds_used`, `staffed_adult_icu_bed_occupancy`, 
            `total_staffed_adult_icu_beds`))

I then checked again for near perfect collinearity among the remaining predictors. I first created a tibble corr_pred_remain containing the correlation coefficients for the remaining predictors arranged in descending order. Then I filtered to see if there is any rows with the absolute value of the correlation coefficient greater than 0.9:

# remaining predictors correlations
corr_pred_remain <- covid_data %>% 
  # unselect outcome variable
  select(-c(critical_staffing_shortage_today_yes)) %>% 
  # temporarily change `state` and `date` to type numeric
  mutate(date = as.numeric(date),
         # first turn state into a factor
         # then turn it into a numeric variable
         # with values determined by factor levels
         state = as.numeric(as.factor(state))) %>%
  # remove rows with missing data
  drop_na() %>%
  # correlation matrix
  correlate() %>% 
  # turn into a tibble
  stretch() %>% 
  rename("correlation" = "r") %>% 
  # arrange in descending order of correlation
  arrange(desc(correlation))

# show tibble
kbl(corr_pred_remain) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "200px")

x	y	correlation
inpatient_beds	inpatient_beds_coverage	0.8815523
inpatient_beds_coverage	inpatient_beds	0.8815523
inpatient_beds	inpatient_beds_used_covid	0.7889578
inpatient_beds_used_covid	inpatient_beds	0.7889578
inpatient_beds_coverage	inpatient_beds_used_covid	0.7513113
inpatient_beds_used_covid	inpatient_beds_coverage	0.7513113
inpatient_beds_utilization	inpatient_beds_used_covid	0.2566885
inpatient_beds_used_covid	inpatient_beds_utilization	0.2566885
inpatient_beds	inpatient_beds_utilization	0.1966966
inpatient_beds_utilization	inpatient_beds	0.1966966
date	inpatient_beds_used_covid	0.1630853
inpatient_beds_used_covid	date	0.1630853
inpatient_beds_utilization	inpatient_beds_coverage	0.1335302
inpatient_beds_coverage	inpatient_beds_utilization	0.1335302
date	inpatient_beds_utilization	0.1304958
inpatient_beds_utilization	date	0.1304958
inpatient_beds_utilization	adult_icu_bed_utilization	0.1049237
adult_icu_bed_utilization	inpatient_beds_utilization	0.1049237
date	inpatient_beds_coverage	0.0734227
inpatient_beds_coverage	date	0.0734227
adult_icu_bed_utilization	inpatient_beds_used_covid	0.0730032
inpatient_beds_used_covid	adult_icu_bed_utilization	0.0730032
adult_icu_bed_utilization	inpatient_beds_coverage	0.0718558
inpatient_beds_coverage	adult_icu_bed_utilization	0.0718558
inpatient_beds	adult_icu_bed_utilization	0.0502165
adult_icu_bed_utilization	inpatient_beds	0.0502165
date	inpatient_beds	0.0501876
inpatient_beds	date	0.0501876
date	adult_icu_bed_utilization	0.0335863
adult_icu_bed_utilization	date	0.0335863
state	date	-0.0031131
date	state	-0.0031131
state	inpatient_beds_coverage	-0.0394746
inpatient_beds_coverage	state	-0.0394746
state	adult_icu_bed_utilization	-0.0471160
adult_icu_bed_utilization	state	-0.0471160
state	inpatient_beds	-0.0857746
inpatient_beds	state	-0.0857746
state	inpatient_beds_used_covid	-0.0989921
inpatient_beds_used_covid	state	-0.0989921
state	inpatient_beds_utilization	-0.1613285
inpatient_beds_utilization	state	-0.1613285
state	state	NA
date	date	NA
inpatient_beds	inpatient_beds	NA
inpatient_beds_utilization	inpatient_beds_utilization	NA
adult_icu_bed_utilization	adult_icu_bed_utilization	NA
inpatient_beds_coverage	inpatient_beds_coverage	NA
inpatient_beds_used_covid	inpatient_beds_used_covid	NA

# check for correlation exceeding 0.9
corr_pred_remain %>% 
  filter(abs(correlation) > 0.9) %>% 
  nrow()

## [1] 0

As shown above, there is no correlation values exceeding 0.9.

I also created a correlation plot for the remaining predictors and the outcome variable, temporarily turning state and date into numeric variables:

# correlation plot between predictors
covid_data %>% 
  # temporarily change `state` and `date` to type numeric
  mutate(date = as.numeric(date),
         # first turn state into a factor
         # then turn it into a numeric variable
         # with values determined by factor levels
         state = as.numeric(as.factor(state))) %>%
  # remove rows with missing data
  drop_na() %>% 
  # compute correlation matrix
  cor() %>% 
  # visualize
  corrplot(type = "lower", tl.srt = 45,  tl.cex = 0.5,
           method = "circle", tl.col = 'black',
           order = "hclust")

As shown, there are a few strong correlations (above 0.8) between variables inpatient_beds, inpatient_beds_used_covid, and inpatient_beds_coverage, but there is no near perfect collinearity. Also, there is no strong direct relationship between the response variable and some of the predictors.

Missing Values

After determining the set of predictors, I look at the missing values. During initial inspection using skimr functions, I learned that the outcome variable, critical_staffing_shortage_today_yes, does not have any missing data. To start the analysis of missing data, I provided a visualization of the overall situation of missingness in the dataset after determining the set of predictors:

# overview of the missingness situation
covid_data %>% 
  vis_miss(cluster = TRUE)

As shown, after filtering, there are 8 variables in the dataset including the outcome variable. While many variables have near 100% completion rate, variable adult_icu_bed_utilization has around 38% missing values.

I also visualized the distribution of percentage of missingness among the predictors. To do so, I first obtained a tibble of the numerical summaries for missing data in covid_data using miss_var_summary(). Then I created a histogram for the distribution of pct_miss.

# summary for missing data for predictors
pred_miss_summary <- covid_data %>% 
  select(-critical_staffing_shortage_today_yes) %>% 
  miss_var_summary()

# visualize the distribution of percentage of missing values 
pred_miss_summary %>% 
  ggplot(aes(pct_miss)) + 
  # add histogram
  geom_histogram() +
  labs(
    x = "Percent Missing",
    title = "Distribution of the Percentage of Missingness"
  )

As shown, most variables have close to 100% completion rate. Also, no variable has missing rate above 40%, which allows them to convey a valuable amount of information. Thus, there is no need to exclude any variables in the later analysis due to severe missingness. I initially hypothesized that the missing data might represent a value of 0. However, the dataset dictionary and observations from the initial inspection indicate that NA values and explicit 0 values are not equivalent for this dataset. Also, the dataset dictionary suggests that “no statistical analysis is applied to account for non-response and/or to account for missing data”. Thus, for the convenience of later analysis, I chose to filter out observations with missing values.

# remove rows containing NA values
covid_data <- covid_data %>% 
  drop_na()

Exploring Timeseries - the date Variable

Since the dataset is considered as a timeseries, the date variable is an important focus of the analysis. The exploration in this section aims to determine the time range of the data used for modeling and relation between date and the outcome variable of the prediction.

Determine Time Range

Since the situations regarding the trends of confirmed and suspected cases and the patterns in medical resource usage change rapidly overtime, including data from very early days might not be very valuable for the later statistical learning process. Thus, I chose to include only the most recent observations. During initial skimming, I noticed that the more distant times have fewer complete observations. Thus, I chose to exclude observations from the earlier period of time that has significantly fewer complete observations than the later times. To determine the “cutting point” for the time range of the observations to be used, I count the number of observations at each date after removing rows with missing data. The visualization is shown below:

# visualize the distribution of valid observations overtime
covid_data %>% 
  ggplot(aes(date)) + 
  geom_histogram() + 
  labs(
    title = "Number of Observations at Each Date"
  )

As shown, the dates before August 2020 have significantly less number of observations. Matching the observations from initial skimming, these dates are also more distant dates, I chose to not include them in the later modeling. From now on, the observations in the dataset are on dates later than 2020-08-01.

# filter out dates
covid_data <- covid_data %>% 
  filter(date >= "2020-08-01")

I also examined the relation between the outcome variable and date to see whether there is straight linear relation between them:

# relation between response variable and `date`
covid_data %>% 
  ggplot(aes(date, critical_staffing_shortage_today_yes)) + 
  geom_point() + 
  labs(
    title = "Relation between the Response Variable and Date", 
    subtitle = "critical_staffing_shortage_today_yes",
    x = "Date", 
    y = "Hospitals with Critical Staffing Shortages"
  )

The absence of any obvious linear pattern suggests that there date does not have a straight-linear relation with the outcome variable.

Categorical Variable

I also inspected the categorical predictor state to determine whether it is necessary to alter factor levels before encoding:

# visualize distribution of `state`
covid_data %>% 
  ggplot(aes(y = state)) + 
  geom_bar() + 
  xlim(0, 250) + 
  labs(y = NULL, 
       title = "Number of Observations for Different State")

As shown, the number of observations in all 52 levels of state are evenly distributed. However, since the large number of levels might lead to high dimensionality and a sparse matrix when encoding, I chose to collapse it into regions. From now on, the state_region variable represents the region where the state is located according to the common way of referring to regions in the United States by grouping them into 5 regions according to their geographic position on the continent (the Northeast, Southwest, West, Southeast, and Midwest). The way of classifying the regions is obtained on the National Geographic’s website. I put “DC” (capital), “VI” (Virgin Islands), “PR” (Puerto Rico), and “HI” (Hawaii) into the other category.

# collapsing `state` levels to regions
covid_data <- covid_data %>% 
  mutate(state = 
           fct_collapse(state, "Northeast" = c("ME", "VT", "NH", "MA", 
                                               "NY", "RI", "CT", "NJ", "PA"), 
                        "Midwest" = c("ND", "SD", "MN", "WI", "MI", "IA", 
                                      "IL", "IN", "OH", "NE", "KS", "MO"), 
                        "Southeast" = c("MD", "DE", "WV", "VA", "KY", "TN", 
                                        "NC", "SC", "GA", "AL", "MS", "AR",
                                        "LA", "FL"), 
                        "Southwest" =c("AZ", "NM", "TX", "OK"), 
                        "West" = c("AK", "WA", "OR", "MT", "ID", 
                                   "WY", "CA", "NV", "UT", "CO"), 
                        "other" = c("PR", "VI", "DC", "HI"))) %>% 
  rename(state_region = state)

Response Variable

I then visualized the distribution of the output variable:

# visualize outcome var
covid_data %>% 
  ggplot(aes(critical_staffing_shortage_today_yes)) + 
  geom_histogram() + 
  labs(
    title = "Distribution of Response Variable", 
    subtitle = "critical_staffing_shortage_today_yes",
    x = "Number of Hospitals Reporting Critical Staff Shortage"
  )

The response variable is right-skewed, meaning that there are more observations with smaller number of hospitals having a critical staff shortage than observations with very large number of hospitals having a critical staff shortage. The skewness leads me to consider using stratified sampling in the later splitting and also log-transform it. I replaced the original variable critical_staffing_shortage_today_yes with a new variable critical_shortage_log, obtained through log-transformation using base 10. From this point on, the outcome variable is critical_shortage_log, the log-transformed number of hospitals having a critical staffing shortage in a state at a given date:

# log-transform outcome var
covid_data <- covid_data %>% 
  mutate(
    critical_shortage_log = 
      log10(critical_staffing_shortage_today_yes + 0.00000001)
  ) %>% 
  select(-critical_staffing_shortage_today_yes)

Store Processed Data

After finalizing the tidying and exploration, I stored the processed dataset as a .rds file in the processed folder (the code for this process is shown below with eval set to FALSE):

# store processed data
covid_data %>% 
  write_rds("data/processed/covid_data.rds")

Section Summary - EDA

The Exploratory Data Analysis (EDA) section examines the key features and patterns in the original unprocessed dataset for data tidying, predictor selection, and gathering information that facilitates the later modeling process.

The EDA section explores the correlation between variables, analyzes the missing data, narrows down the time range of the observations used for modeling, and visualizes the distribution of the response variable.

Through the exploration, 7 variables from the original dataset are selected as predictors and rows with NA values are removed. The skewness of the outcome variable implies the need for stratified sampling and log-transformation. The original variable critical_staffing_shortage_today_yes was log-transformed to obtain a new variable critical_shortage_log, the log-base-10-transformed number of hospitals having a critical staffing shortage in a state at a given date, as the new response variable for the later process.

The tidied tibble containing the outcome variable and the 7 predictors are stored in the “processed” folder inside “data”. Among the predictors, one is categorical (state_region), one is date (date), and the rest are numeric. Since date is used as a predictor, time split with stratification on the outcome variable will be applied in the later modeling process.

Predictive Modeling

Predictive Goal and Models of Interest

The goal of the prediction is regression, and the outcome variable is critical_shortage_log, the log-transformed number of hospitals having critical staffing shortage in a state on a specific date.

Four competing model types were trained and tuned:

1. A random forest model (rand_forest()) with the ranger engine;
2. A boosted tree model (boost_tree()) with the xgboost engine;
3. A k-nearest neighbors model (nearest_neighbors()) with the kknn engine;
4. A elastic net regression model (linear_reg()) with the glmnet engine.
   

Load Data

I first loaded in the processed data:

# load data
covid_data <- 
  read_rds("data/processed/covid_data.rds")

Split Data and Cross-Validation

I chose to split the data into 70% training, 30% testing using initial time split with stratified sampling by the outcome variable critical_shortage_log.

# split data
covid_data <- initial_time_split(covid_data, prop = 0.7, 
                                 strata = critical_shortage_log)
# obtain training and test sets
covid_train <- training(covid_data)
covid_test <- testing(covid_data)

I then verified that the training and testing data sets had the appropriate number of observations:

# verify dimensions
dim(covid_train)

## [1] 7828    8

11183 * 0.7

## [1] 7828.1

dim(covid_test)

## [1] 3355    8

11183 * 0.3

## [1] 3354.9

As shown, the number of rows in the training (7828) and test (3355) sets are consistent with the numbers gained when multiplying the total number of observations in covid_data (11183) by their relative proportions (0.7 and 0.3).

Afterwards, I did the V-fold cross-validation with 10 folds, repeated 5 times, to fold the training data:

covid_folds <- 
  vfold_cv(data = covid_train, v = 10, repeats = 5)

Second Round EDA - Inspection on the Training Set

After splitting, I explored the key features of the training set for determining the steps to add when creating the recipe. The EDA section log-transformed the response variable to avoid potential issues caused by right-skewness. Here, the inspection on the training set indicates that variables inpatient_beds, inpatient_beds_coverage, and inpatient_beds_used_covid are also right-skewed. adult_icu_bed_utilization is about normal but slightly left-skewed, inpatient_beds_utilization is about normal.

# distribution of all numeric variables
covid_train %>% 
  select(-c(state_region, date, 
            critical_shortage_log)) %>% 
  # Convert to key-value pairs
  gather() %>% 
  ggplot(aes(value)) + 
  # faceting
  facet_wrap(~ key, scales = "free") + 
  geom_histogram() + 
  labs(
    title = "Distribution of All Numeric Predictors", 
    subtitle = "Using Training Set Data"
  )

The observed skewness led me to consider using step_log() on variables inpatient_beds, inpatient_beds_coverage, and inpatient_beds_used_covid in creating the recipe.

In addition, I explored the distribution of the levels of state_region to determine whether it is necessary to apply step_other() in creating the recipe.

covid_train %>% 
  ggplot(aes(y = state_region)) + 
  geom_bar()

As shown, regions other and Southwest have less than half the numbers of observations of the other regions. Thus, I chose to put the observations in these levels into a “Southwest_and_other” category using step_other() in making the recipe.

Recipe

I then set up a recipe to predict critical_shortage_log with all other variables in the dataset. Due to skewness, I log-transformed inpatient_beds, inpatient_beds_coverage, and inpatient_beds_used_covid using step_log(). To avoid problems caused by 0 values, I set offset to 0.0000001. I put the infrequently occurring values of state_region into an “Southwest_and_other” category and one-hot encoded this categorical predictor. In addition, I applied step_date() on date. Afterwards, I removed the original date column using step_rm(). Then, I standardized all predictors using step_center() and step_scale().

Since I plan to use tree-based models, I prep() and bake() the recipe on the training data to determine the upper limit for the possible values of mtry.

covid_recipe <- 
  recipe(critical_shortage_log ~ ., 
         data = covid_train) %>% 
  # log-transform all numeric predictors
  step_log(c(inpatient_beds, inpatient_beds_coverage, 
             inpatient_beds_used_covid), offset = 0.0000001) %>% 
  step_other(state_region, threshold = 1000, 
             other = "Southwest_and_other") %>% 
  step_date(date, features = "doy") %>% 
  step_rm(date) %>%
  step_dummy(all_nominal(), one_hot = TRUE) %>% 
  # center and scale all predictors
  step_center(all_predictors()) %>% 
  step_scale(all_predictors())
  
# `prep()` and `bake()` recipe on the training data
prep(covid_recipe) %>% 
  bake(new_data = NULL) %>% 
  # show the number of columns to determine upper limit for `mtry`
  ncol()

## [1] 12

When prep() and bake() the recipe on the training data, there are 12 columns in the data after processing, indicating the upper limit of mtry should be no greater than 11.

Model Fitting

This section assesses the performance of different models for the prediction problem of this project. It tuned and trained four model types:

1. A random forest model (rand_forest()) with the ranger engine;
2. A boosted tree model (boost_tree()) with the xgboost engine;
3. A k-nearest neighbors model (nearest_neighbors()) with the kknn engine;
4. A elastic net regression model (linear_reg()) with the glmnet engine.
   

Set up Models and Flag Tuning Parameters

For the random forest model, I tuned the hyper-parameters mtry and min_n. For the boosted tree model, I tuned mtry, min_n, and learn_rate. For the k-nearest neighbors model, I tuned neighbors. For the elastic net regression model, I tuned penalty and mixture. The codes below set up the models and flagged the parameters for tuning.

# train and tune models
# random forest model
rf_model <- rand_forest(mode = "regression",
                        min_n = tune(),
                        mtry = tune()) %>% 
  set_engine("ranger")

# boosted tree model
bt_model <- boost_tree(mode = "regression", 
                       mtry = tune(), 
                       min_n = tune(), 
                       learn_rate = tune()) %>% 
  set_engine("xgboost")

# Nearest neighbors model
nn_model <- nearest_neighbor(mode = "regression", 
                             neighbors = tune()) %>% 
  set_engine("kknn")

# elastic net regression model
elastic_net_reg_model <- linear_reg(penalty = tune(), 
                                    mixture = tune()) %>% 
  set_engine("glmnet")

Grid for Tuning

I then set up and store regular grids with 5 levels of possible values for tuning hyper-parameters for each of the four models. For mtry, I used update() to change the upper limit value to the number of predictor columns. For learn_rate, I set range = c(-1, 0). I set the range of neighbors to be c(1L, 25L). I used default tuning parameters for parameters min_n, mixture, and penalty.

# random forest model
rf_params <- parameters(rf_model) %>% 
  update(mtry = mtry(range = c(1, 11)))
# store regular grid
rf_grid <- grid_regular(rf_params, levels = 5)

# boosted tree model
bt_params <- parameters(bt_model) %>% 
  update(mtry = mtry(range = c(1, 11)), 
         learn_rate = learn_rate(range = c(-1, 0)))
# store regular grid
bt_grid <- grid_regular(bt_params, levels = 5)

# Nearest neighbors model
nn_params <- parameters(nn_model) %>% 
  update(neighbors = neighbors(range = c(1L, 25L)))
# store regular grid
nn_grid <- grid_regular(nn_params, levels = 5)

# elastic net regression model
elastic_net_params <- parameters(elastic_net_reg_model)
# store regular grid
elastic_net_grid <- grid_regular(elastic_net_params, levels = 5)

Workflow

Afterwards, I set up a workflow for each of the 4 competing models (random forest, boosted tree, knn, and elastic net regression):

# random forest model
rf_workflow <- workflow() %>% 
  add_model(rf_model) %>% 
  add_recipe(covid_recipe)

# boosted tree model
bt_workflow <- workflow() %>% 
  add_model(bt_model) %>% 
  add_recipe(covid_recipe)

# Nearest neighbors model
nn_workflow <- workflow() %>% 
  add_model(nn_model) %>% 
  add_recipe(covid_recipe)

# elastic net regression model
elastic_net_workflow <- workflow() %>% 
  add_model(elastic_net_reg_model) %>% 
  add_recipe(covid_recipe)

Tuning Parameters

After setting up the workflow, I used the codes below to tune the parameters for the models and find the values that optimize model performance across folds for each of the workflows. The codes were run in separate R scripts, and the results were read-in using hidden R code chunks.

# tune the parameters
# random forest model
rf_tuned <- rf_workflow %>% 
  tune_grid(covid_folds, grid = rf_grid)

# boosted tree model
bt_tuned <- bt_workflow %>% 
  tune_grid(covid_folds, grid = bt_grid)

# Nearest neighbors model
nn_tuned <- nn_workflow %>% 
  tune_grid(covid_folds, grid = nn_grid)

# elastic net regression model
elastic_net_tuned <- elastic_net_workflow %>% 
  tune_grid(covid_folds, grid = elastic_net_grid)

Tuning Results

I then examined the results of tuning using autoplot() on each of the objects stored from the tuning and training step. I set the metric argument of autoplot() to "rmse" for each to explore the patterns in RMSE as the values of the tuning parameters change:

# checkout results
# random forest model
autoplot(rf_tuned, metric = "rmse")

# boosted tree model
autoplot(bt_tuned, metric = "rmse")

# nearest neighbors model
autoplot(nn_tuned, metric = "rmse")

# elastic net regression model
autoplot(elastic_net_tuned, metric = "rmse")

As shown, for the random forest model, the RMSE value becomes significantly lower when mtry, the number of randomly selected predictors, is larger than 3 in the combinations with all different values of min_n, the minimal node size. For all parameters combinations, the RMSE value is the smallest when mtry is around 6 to 8. The combinations with the smaller min_n values (2 or 11) tends to produce lower RMSE across all different values of mtry.

For the boosted tree model, the RMSE value tends to be smallest when learn_rate is slightly above 0.3 for all combinations. The smallest min_n value gives the lowest RMSE for each parameters combination. For all combinations, the RMSE value is the lowest when mtry is close to 1 or 9.

For the nearest neighbors model, the RMSE value becomes significantly lower for neighbors greater than 5. The RMSE flattens around 0.87 afterwards, and it has the lowest RMSE when neighbors is around 14. The RMSE value shows a slight trend of increasing when neighbors gets above 20.

For the elastic net regression model, the RMSE value flattens at about 1.60 for combinations with all different penalty values and mixture values close to 0. The RMSE value shows a significant increase when mixture gets close to 1 for all parameters combinations. Among them, the parameter combination with the lowest penalty (0.05) has the lowest RMSE value and slowest rate of increasing.

Best Model and Optimal Parameters

To determine the best performed model for the prediction problem of this project, I ran show_best() on each of the four tuned models to look for the smallest RMSE across cross-validation. I also examined the optimum value(s) for the best model’s tuning parameters. Note, in the output tibble column .config is removed for spacing concerns. Also, the row showing the parameter set with the optimal RMSE values for each model is highlighted in blue:

# show rmse and select parameters based on best numerical performance
# random forest model
show_best(rf_tuned, metric = "rmse") %>% 
  select(-.config) %>%
  kbl() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed")) %>% 
  row_spec(1, color = "white",
              background = "blue") %>% 
  kableExtra::footnote(general = "Tuning Result for Random Forest Model")

mtry	min_n	.metric	.estimator	mean	n	std_err
8	11	rmse	standard	0.7832487	50	0.0159351
6	2	rmse	standard	0.7833735	50	0.0158343
8	2	rmse	standard	0.7847199	50	0.0163364
6	11	rmse	standard	0.7848914	50	0.0156177
8	21	rmse	standard	0.7970609	50	0.0156247
Note:
Tuning Result for Random Forest Model

# boosted tree model
show_best(bt_tuned, metric = "rmse") %>% 
  select(-.config) %>%
  kbl() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed")) %>% 
  row_spec(1, color = "white",
              background = "blue") %>% 
  kableExtra::footnote(general = "Tuning Result for Boosted Tree Model")

mtry	min_n	learn_rate	.metric	.estimator	mean	n	std_err
8	2	0.3162278	rmse	standard	0.8353934	50	0.0157226
1	2	0.3162278	rmse	standard	0.8356343	50	0.0170599
11	2	0.3162278	rmse	standard	0.8356343	50	0.0170599
8	11	0.3162278	rmse	standard	0.8425950	50	0.0140361
1	11	0.3162278	rmse	standard	0.8450116	50	0.0145884
Note:
Tuning Result for Boosted Tree Model

# nearest neighbors model
show_best(nn_tuned, metric = "rmse") %>% 
  select(-.config) %>%
  kbl() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed")) %>% 
  row_spec(1, color = "white",
              background = "blue") %>% 
  kableExtra::footnote(general = "Tuning Result for k-Nearest Neighbors Model")

neighbors	.metric	.estimator	mean	n	std_err
13	rmse	standard	0.8578635	50	0.0158085
19	rmse	standard	0.8607880	50	0.0153920
25	rmse	standard	0.8663083	50	0.0151179
7	rmse	standard	0.8704585	50	0.0166701
1	rmse	standard	1.0816899	50	0.0210416
Note:
Tuning Result for k-Nearest Neighbors Model

# elastic net regression model
show_best(elastic_net_tuned, metric = "rmse") %>% 
  select(-.config) %>%
  kbl() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed")) %>% 
  row_spec(1, color = "white",
              background = "blue") %>% 
  kableExtra::footnote(general = "Tuning Result for Elastic Net Regression Model")

penalty	mixture	.metric	.estimator	mean	n	std_err
0e+00	1.0000	rmse	standard	1.606812	50	0.0124028
0e+00	1.0000	rmse	standard	1.606812	50	0.0124028
1e-05	1.0000	rmse	standard	1.606812	50	0.0124028
0e+00	0.2875	rmse	standard	1.606813	50	0.0123960
0e+00	0.2875	rmse	standard	1.606813	50	0.0123960
Note:
Tuning Result for Elastic Net Regression Model

As shown above, the random forest model produced the smallest RMSE across cross-validation. Here, the mean RMSE value of the best tuning parameters combination for the random forest model is 0.783, which is the lowest among the 4 models. Also, the standard error of its RMSE value is 0.01593507, and the difference between the mean RMSE of the best tuning parameters combination of the random forest model and the second lowest mean RMSE (the RMSE of the boosted tree model) is 0.052. Since the standard error of the random forest model’s RMSE is much smaller than its difference with the second lowest mean RMSE, the random forest model model shows significantly better performance in producing the lowest bias on average. Thus, I concluded that the random model has performed the best.

The optimum values for the random forest parameters are: mtry equals 8 and min_n equals 11.

Fit Entire Training Set

I then fit the winning model to the entire training set:

rf_workflow_tuned <- rf_workflow %>% 
  finalize_workflow(select_best(rf_tuned, metric = "rmse"))

rf_results <- fit(rf_workflow_tuned, covid_train)

Fit Testing Set

To examine the chosen model’s performance on the brand-new, untouched testing dataset, I used predict(), bind_cols(), and metric_set() to fit the tuned model to the covid_test. Since the scale of the outcome variable is log-transformed, I transformed it back to its original scale for better interpretation.

# create metric set
covid_metric <- yardstick::metric_set(yardstick::rmse, yardstick::mae, 
                                      yardstick::rsq)

# show result of prediction on testing data
predict(rf_results, new_data = covid_test) %>% 
  # change the predicted value from log-scale to original scale
  mutate(
    new_pred = round(10 ^ .pred)
  ) %>% 
  bind_cols(covid_test %>% select(critical_shortage_log)) %>% 
  # transform from log-scale back to original scale
  mutate(truth_obs = round(10 ^ critical_shortage_log)) %>%
  covid_metric(truth = truth_obs, estimate = new_pred) %>% 
  kbl() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"))

.metric	.estimator	.estimate
rmse	standard	9.4717715
mae	standard	4.7529061
rsq	standard	0.8224842

As shown, the RMSE value is 9.47, meaning that when applying the model on the test set, the average bias is about 9 hospitals. This value is pretty high. The RMSE value measures the average squared difference between the estimated values and the actual value. Considering the extreme right-skewness of the outcome variable observed in the EDA section, the relatively high RMSE might be caused by several outliers with extreme values. The r-squared value is 0.8225, meaning that about 82.25% of the variation in the outcome can be explained by the model. The mae value is 4.753, suggesting that the average absolute differences between prediction and actual observations is about 4 or 5 hospitals. Even though the RMSE value is high, the relatively high r-squared value indicates the model’s adequate performance in explaining the variances in the response variable. Thus, taken into consideration the impact of the possible presence of large outliers on the RMSE value and the good r-squared value, I concluded that the model’s performance in making predictions using the test set is relatively adequate.

Summary and Future Direction

Model Fitting Results

In this project, four competing types of models are trained and tuned using cross-validation. In statistical learning or machine learning, we are generally interested in getting predictions with the lowest possible bias on average. Thus, I picked the method with optimal (lowest) RMSE value. Among the competing models, the random forest model (rand_forest()) with the ranger engine shows the lowest RMSE value with optimal parameters mtry equals 8 and min_n equals 11. Therefore, it was chosen to be the winning model.

The original dataset contains many outliers, and random forest is robust to outliers. Also, in the EDA section, I observed that some variables, especially date, did not have a straight-linear relation with the outcome variable. Also, date does not have a direct linear relation with other predictor variables. The non-linearity makes random forest a favorable model in comparison to the linear algorithms. In addition, the predictor state_region is categorical while other predictor variables are continuous. Since random forest works well with both categorical and continuous variables, it showed better performance in the situation of this problem.

The predictions and truth values were transformed from log-base10 scale back to normal scale after fitting the winning model to the testing dataset for the ease of comparison and interpretation. The RMSE value is 9.47, meaning that the average bias is about 9 hospitals. The r-squared value is 0.8225, indicating that about 82.25% of the variation in the outcome variable can be explained by the model. The mae value is 4.753, suggesting that the average absolute differences between prediction and actual observations is about 4 or 5 hospitals.

The RMSE value is pretty high, considering the context that many true observations have values lower than 50 based on the visualization from the EDA section. The high RMSE might be caused by the presence of large outliers. Taken into account the relatively high r-squared value (82.25%), the model’s performance in making predictions using on test set is mildly satisfactory, since it successfully explains a large proportion of the variances in the response variable, despite having a relatively high bias.

Next Steps

Reading online documentation, I learned that random forest can automatically handle missing values. However, for this project, I removed all rows with NA values in the EDA section before model tuning. For further exploration on the models’ performances, it might be helpful to not drop the NA values and access different model’s performance in handling missing values.

Also, even though the dataset is a time series, no obvious relation between date and any of the other variables in the dataset was observed in the EDA section. Thus, it might be interesting to run the predictions again without considering the effect of date on the outcome variable and compare the two results. This approach involves using initial_split() instead of initial_time_split().

Moreover, the state variable is collapsed into state_region to reduce the number of levels for the convenience of modeling. To access whether this change impacts a model’s performance, future study can use feature hashing in creating the recipe for encoding the 52 levels of the state variable instead of collapsing them into regions.

Lastly, the original outcome variable before log-transformation, critical_staffing_shortage_today_yes, is a count variable that takes only positive whole number values. However, it does not have a finite set of values, since the total number of hospitals in each state region is different and hard to access. Thus, it cannot be treated as a multi-level categorical variable. From online resources, I learned that the count variables are best predicted by the poisson regression model. However, since this type of model is not yet covered in class, I treated the outcome variable as a numeric variable for the predictive modeling for this project. For future challenges, it might be helpful to do the prediction with a poisson regression model and compare its performance with the other models covered in this project.

Conclusion

This project focuses on data modeling and analysis of the COVID-19 Reported Patient Impact and Hospital Capacity by State Timeseries dataset. The data contains information regarding the COVID-19 related patient impact and hospital utilization as state-specific timeseries from 2020-01-01 to 2021-02-27.

The goal of the project is to predict the number of hospitals reporting a critical staffing shortage in a state at a specific day (variable critical_staffing_shortage_today_yes in the original dataset), given its current situation regarding utilization of hospital resources and medical system capacity.

The EDA section discovered the high collinearity between many predictor variables and the right-skewness of the outcome variable. Data tidying on the original dataset was used to reduce predictors with near perfect collinearity and to fix the problem of skewness in the outcome variable.

The modeling section trained and tuned four types of models for regression prediction. Among them, the random forest model (rand_forest()) with the ranger engine shows the lowest RMSE value with optimal parameters mtry equals 8 and min_n equals 11, and it is chosen to be the winning model. The chosen model is then fit to the entire training set and the test set afterwards for final assessment of its performance. Using the testing set, the model has a RMSE value of 9.47, a r-squared value of 0.8225, and a mae value is 4.753. The model’s performance in predicting the brand-new test set is adequate, despite having a relatively high RMSE value , since it successfully explains a large proportion of the variances in the response variable.

Based on the results, observations, and limitations of the current project, future studies can be conducted to further access the impact of the date variable on the outcome, examine effects of changing the levels of the state variable, and explore the use of poisson regression in predicting count numbers.

Citations

1. Phelan AL, Katz R, Gostin LO. The Novel Coronavirus Originating in Wuhan, China: Challenges for Global Health Governance. JAMA. 2020 Feb 25;323(8):709-710. doi: 10.1001/jama.2020.1097. PMID: 31999307.